Maths-
General
Easy

Question

After the first raffle drawing 497 tickets remain. After the second raffle drawing, 494 tickets remain. Assuming that the pattern continues, write an explicit formula for arithmetic sequence to represent the number of raffle tickets that remain after each drawing. How many tickets remain in the bag after the seventh raffle drawing?

Hint:

  • A sequence is said to be arithmetic if the common difference is always constant.
  • The General formula of any AP is a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d.

The correct answer is: a_n=479.


    Explanation:
    • We have given after the first raffle drawing, 497 tickets remain. After the second raffle drawing, 494 tickets remain. Assuming that the pattern continues.
    • We have to find an explicit formula for arithmetic sequence to represent the number of raffle tickets that remain after each drawing. How many tickets remain in the bag after the seventh raffle drawing?
    Step 1 of 2:
    We have given after the first raffle drawing, 497 tickets remain. After the second raffle drawing, 494 tickets remain. Assuming that the pattern continues.
    It will  form an AP with common difference

    494 - 497 = -3
    And First term is 497.
    Now the explicit formula will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 497 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 3 right parenthesis end cell row cell a subscript n equals 500 minus 3 n end cell end table
    Step 2 of 2:
    After 7th raffle drawing the ticket remains will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 500 minus 3 n end cell row cell a subscript n equals 500 minus 3 left parenthesis 7 right parenthesis end cell row cell a subscript n equals 479. end cell end table

    Related Questions to study

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    Use long division to rewrite each rational function, What are the asymptotes of  f ? Sketch the graph.
    F left parenthesis x right parenthesis equals fraction numerator 2 x over denominator x plus 4 end fraction

    1.Find the asymptotes of the rational function, if any.
    2.Draw the asymptotes as dotted lines.
    3.Find the 
    x -intercept (s) and y -intercept of the rational function, if any.
    4.Find the values of y for several different values of x .
    5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x + 4= 0
    x = -4
    The vertical asymptote of the rational function is x= -4
    We will find more points on the function and graph the function.


    From the graph we can analyze that the vertical asymptote of the rational function is  x= -4 and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 2 over 1=2

    Use long division to rewrite each rational function, What are the asymptotes of  f ? Sketch the graph.
    F left parenthesis x right parenthesis equals fraction numerator 2 x over denominator x plus 4 end fraction

    Maths-General
    1.Find the asymptotes of the rational function, if any.
    2.Draw the asymptotes as dotted lines.
    3.Find the x -intercept (s) and y -intercept of the rational function, if any.
    4.Find the values of y for several different values of x .
    5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x + 4= 0
    x = -4
    The vertical asymptote of the rational function is x= -4
    We will find more points on the function and graph the function.


    From the graph we can analyze that the vertical asymptote of the rational function is  x= -4 and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 2 over 1=2
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    In a trail map, the equation y = 1 half x space plus space 1 represents the Tamiami Trail. Choose the equation for a perpendicular trail.
    y equals 1 half x plus 5

    • We have been given the trail map equation of y-axis in the question.
    • We have to choose the equation for a perpendicular trail from the given four options.
    Step 1 of 1:
    We have given an equation y equals 1 half x plus 1
    We have to find equation of line which is perpendicular to given line y equals 1 half x plus 5
    Its slope is equal to given line.
    So, it is parallel not perpendicular.

    In a trail map, the equation y = 1 half x space plus space 1 represents the Tamiami Trail. Choose the equation for a perpendicular trail.
    y equals 1 half x plus 5

    Maths-General
    • We have been given the trail map equation of y-axis in the question.
    • We have to choose the equation for a perpendicular trail from the given four options.
    Step 1 of 1:
    We have given an equation y equals 1 half x plus 1
    We have to find equation of line which is perpendicular to given line y equals 1 half x plus 5
    Its slope is equal to given line.
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    Maths-

    A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Graph the sequence for the first 5 rows.

    • A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it
    • We have to find the graph of the sequence for the first 5 rows
    Step 1 of 1:
    Here it will be an AP, with first term 14 and common difference 2.
    So, The explicit formula will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 14 plus left parenthesis n minus 1 right parenthesis 2 end cell row cell a subscript n equals 12 plus 2 n end cell end table
    Now the graph will be

    A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Graph the sequence for the first 5 rows.

    Maths-General
    • A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it
    • We have to find the graph of the sequence for the first 5 rows
    Step 1 of 1:
    Here it will be an AP, with first term 14 and common difference 2.
    So, The explicit formula will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 14 plus left parenthesis n minus 1 right parenthesis 2 end cell row cell a subscript n equals 12 plus 2 n end cell end table
    Now the graph will be

    parallel
    General
    Maths-

    Juanita is trying to determine the vertical and horizontal asymptotes for the graph of  the function  f left parenthesis x right parenthesis equals fraction numerator x squared plus 3 x minus 4 over denominator x squared minus x minus 12 end fraction. Describe and correct the error Juanita made in determining the vertical and horizontal asymptotes.

    1.Find the asymptotes of the rational function, if any.
    2.Draw the asymptotes as dotted lines.
    3.Find the 
    x -intercept (s) and y -intercept of the rational function, if any.
    4.Find the values of y for several different values of x .
    5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x2 – x - 12= 0
    x2 – 4x + 3x - 12= 0
    x(x - 4) + 3(x - 4) = 0
    (x - 4)(x + 3)
    x = -3 and x =4
    The vertical asymptote of the rational function is x= -3 and x= 4
    horizontal asymptote is
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    Juanita has taken the horizontal asymptote as y = -4 is an error in her calculation.

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    Maths-General
    1.Find the asymptotes of the rational function, if any.
    2.Draw the asymptotes as dotted lines.
    3.Find the x -intercept (s) and y -intercept of the rational function, if any.
    4.Find the values of y for several different values of x .
    5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x2 – x - 12= 0
    x2 – 4x + 3x - 12= 0
    x(x - 4) + 3(x - 4) = 0
    (x - 4)(x + 3)
    x = -3 and x =4
    The vertical asymptote of the rational function is x= -3 and x= 4
    horizontal asymptote is
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    A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Write an explicit  formula to represent the number of chairs in the nth row.

    • A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it
    • We have to find the explicit formula to represent the number of chairs in the nth row.
    Step 1 of 1:
    Here it will be an AP, with first term 14 and common difference 2.
    So, The explicit formula will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 14 plus left parenthesis n minus 1 right parenthesis 2 end cell row cell a subscript n equals 12 plus 2 n end cell end table

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    • A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it
    • We have to find the explicit formula to represent the number of chairs in the nth row.
    Step 1 of 1:
    Here it will be an AP, with first term 14 and common difference 2.
    So, The explicit formula will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 14 plus left parenthesis n minus 1 right parenthesis 2 end cell row cell a subscript n equals 12 plus 2 n end cell end table

    General
    Maths-

    A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Write a recursive formula to represent the number of chairs in the nth row.

    • A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it
    • We have to find the recursive formula to represent the number of chairs in the nth row.
    Step 1 of 1:
    Here it will be an AP, with common difference 2.
    So, The recursive formula will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals a subscript n minus 1 end subscript plus d end cell row cell a subscript n equals a subscript n minus 1 end subscript plus 2 end cell end table

    A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Write a recursive formula to represent the number of chairs in the nth row.

    Maths-General
    • A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it
    • We have to find the recursive formula to represent the number of chairs in the nth row.
    Step 1 of 1:
    Here it will be an AP, with common difference 2.
    So, The recursive formula will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals a subscript n minus 1 end subscript plus d end cell row cell a subscript n equals a subscript n minus 1 end subscript plus 2 end cell end table

    parallel
    General
    Maths-

    Are graphs of the equations parallel, perpendicular or neither?
    negative 2 x plus 5 y equals negative 4 semicolon space y equals negative 5 over 2 x plus 6

    • We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
    Step 1 of 1:
    We have given two equations

    negative 2 x plus 5 y equals negative 4

    y equals fraction numerator negative 5 over denominator 2 end fraction x plus 6
    Slope of both lines are 2 over 5 comma fraction numerator negative 5 over denominator 2 end fraction respectively
    Since slope are not equal then both are not parallel.
    Product of both slope is 2 over 5 cross times fraction numerator negative 5 over denominator 2 end fraction equals negative 1
    So, both are not perpendicular also.
    So,
    Both are nor parallel neither perpendicular.

    Are graphs of the equations parallel, perpendicular or neither?
    negative 2 x plus 5 y equals negative 4 semicolon space y equals negative 5 over 2 x plus 6

    Maths-General
    • We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
    Step 1 of 1:
    We have given two equations

    negative 2 x plus 5 y equals negative 4

    y equals fraction numerator negative 5 over denominator 2 end fraction x plus 6
    Slope of both lines are 2 over 5 comma fraction numerator negative 5 over denominator 2 end fraction respectively
    Since slope are not equal then both are not parallel.
    Product of both slope is 2 over 5 cross times fraction numerator negative 5 over denominator 2 end fraction equals negative 1
    So, both are not perpendicular also.
    So,
    Both are nor parallel neither perpendicular.

    General
    Maths-

    Casey opened a saving account with a $50 deposit. For every month after the first month she deposits $25. Write an explicit rule to represent the amount of money being deposited in her account. How much money will Casey have in her account after 24 months?

    • We have given Casey opened a saving account with $50 deposit. For every month after the first month she deposits $25.
    • We have to find the explicit rule to represent the amount of money and total amount after 24 months.
    Step 1 of 2:
    In the first month $50 deposited and after that every month $25 will deposits.
    So, This will form an AP.
    So, The explicit form will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 50 plus left parenthesis n minus 1 right parenthesis 25 end cell row cell a subscript n equals 25 plus 25 n end cell end table
    Step 2 of 2:
    After 24 months the amount will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 25 plus 25 n end cell row cell a subscript n equals 25 plus 25 left parenthesis 24 right parenthesis end cell row cell a subscript n equals 25 plus 600 end cell row cell a subscript n equals 625. end cell end table

    Casey opened a saving account with a $50 deposit. For every month after the first month she deposits $25. Write an explicit rule to represent the amount of money being deposited in her account. How much money will Casey have in her account after 24 months?

    Maths-General
    • We have given Casey opened a saving account with $50 deposit. For every month after the first month she deposits $25.
    • We have to find the explicit rule to represent the amount of money and total amount after 24 months.
    Step 1 of 2:
    In the first month $50 deposited and after that every month $25 will deposits.
    So, This will form an AP.
    So, The explicit form will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 50 plus left parenthesis n minus 1 right parenthesis 25 end cell row cell a subscript n equals 25 plus 25 n end cell end table
    Step 2 of 2:
    After 24 months the amount will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 25 plus 25 n end cell row cell a subscript n equals 25 plus 25 left parenthesis 24 right parenthesis end cell row cell a subscript n equals 25 plus 600 end cell row cell a subscript n equals 625. end cell end table

    General
    Maths-

    Are graphs of the equations parallel, perpendicular or neither?
    x equals 4 semicolon space y equals 4

    • We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
    Step 1 of 1:
    We have given two equations

    x = 4
    y = 4
    One line is parallel to y-axis and another line is parallel to x-axis
    So, Both are perpendicular.

    Are graphs of the equations parallel, perpendicular or neither?
    x equals 4 semicolon space y equals 4

    Maths-General
    • We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
    Step 1 of 1:
    We have given two equations

    x = 4
    y = 4
    One line is parallel to y-axis and another line is parallel to x-axis
    So, Both are perpendicular.

    parallel
    General
    Maths-

    Are graphs of the equations parallel, perpendicular or neither?
    y equals 1 half semicolon space y equals negative 3

    • We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
    Step 1 of 1:
    We have given two equations

    y = 1 half

    y = -3
    Slope of both lines are 0,0 respectively
    Since slope are equal then both are parallel.

    Are graphs of the equations parallel, perpendicular or neither?
    y equals 1 half semicolon space y equals negative 3

    Maths-General
    • We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
    Step 1 of 1:
    We have given two equations

    y = 1 half

    y = -3
    Slope of both lines are 0,0 respectively
    Since slope are equal then both are parallel.

    General
    Maths-

    What is the horizontal asymptote of the rational function
    straight F left parenthesis straight x right parenthesis equals fraction numerator a x squared plus b x plus c over denominator d x squared plus e x plus f end fraction

    A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) =fraction numerator p left parenthesis x right parenthesis over denominator q left parenthesis x right parenthesis end fraction, where p(x) and q(x) are polynomials such that q(x) ≠ 0.
    Rational functions are of the form y = f(x)y = fx , where f(x)fx is a 
    rational expression .
    • If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote.
    • If the degree of the numerator is less than the denominator, then the asymptote is located at y = 0 (which is the x-axis).
    • If the degree of the numerator is greater than the denominator, then there is no horizontal asymptote.
    For the given function both the polynomials have the same degree, divide the coefficients of the leading terms.
    y = a / d

    What is the horizontal asymptote of the rational function
    straight F left parenthesis straight x right parenthesis equals fraction numerator a x squared plus b x plus c over denominator d x squared plus e x plus f end fraction

    Maths-General
    A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) =fraction numerator p left parenthesis x right parenthesis over denominator q left parenthesis x right parenthesis end fraction, where p(x) and q(x) are polynomials such that q(x) ≠ 0.
    Rational functions are of the form y = f(x)y = fx , where f(x)fx is a rational expression .
    • If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote.
    • If the degree of the numerator is less than the denominator, then the asymptote is located at y = 0 (which is the x-axis).
    • If the degree of the numerator is greater than the denominator, then there is no horizontal asymptote.
    For the given function both the polynomials have the same degree, divide the coefficients of the leading terms.
    y = a / d
    General
    Maths-

    Are graphs of the equations parallel, perpendicular or neither?
    y = 2x + 1; 2x - y = 3

    • We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
    Step 1 of 1:
    We have given two equations

    y = 2x + 1
    2x - y = 3
    Slope of both lines are 2, 2 respectively
    Since slope are equal then both are parallel.

    Are graphs of the equations parallel, perpendicular or neither?
    y = 2x + 1; 2x - y = 3

    Maths-General
    • We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
    Step 1 of 1:
    We have given two equations

    y = 2x + 1
    2x - y = 3
    Slope of both lines are 2, 2 respectively
    Since slope are equal then both are parallel.

    parallel
    General
    Maths-

    A Trainer mixed water with an electrolyte solution. Container is having 12 gal of 25%  electrolyte solution. The Concentration of electrolytes can be modelled byf left parenthesis x right parenthesis equals fraction numerator 4 over denominator x plus 12 end fraction  , Graph the function.

    1.Find the asymptotes of the rational function, if any.
    2.Draw the asymptotes as dotted lines.
    3.Find the 
    x -intercept (s) and y -intercept of the rational function, if any.
    4.Find the values of y for several different values of x .
    5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x + 12= 0
    x = -12
    The vertical asymptote of the rational function is x= -12
    We will find more points on the function and graph the function.


    From the graph we can analyze that the vertical asymptote of the rational function is  x= -4 and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 2 over 1=2

    A Trainer mixed water with an electrolyte solution. Container is having 12 gal of 25%  electrolyte solution. The Concentration of electrolytes can be modelled byf left parenthesis x right parenthesis equals fraction numerator 4 over denominator x plus 12 end fraction  , Graph the function.

    Maths-General
    1.Find the asymptotes of the rational function, if any.
    2.Draw the asymptotes as dotted lines.
    3.Find the x -intercept (s) and y -intercept of the rational function, if any.
    4.Find the values of y for several different values of x .
    5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x + 12= 0
    x = -12
    The vertical asymptote of the rational function is x= -12
    We will find more points on the function and graph the function.


    From the graph we can analyze that the vertical asymptote of the rational function is  x= -4 and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 2 over 1=2
    General
    Maths-

    Find the 12th term. -8, -5.5 , -3, -0.5, 2.0,....

    • We have given a sequence -8, -5.5, -3, -0.5, 2.0,...
    • We have to find weather the given sequence is AP or not
    Step 1 of 1:
    We have given a sequence -8, -5.5, -3, -0.5, 2.0,...
    The given sequence is an AP
    And we know the recursive formula of any AP is a subscript n equals a subscript n minus 1 end subscript plus d.
    Where d is common difference.
    Here the common difference is 3.5.
    So, The recursive formula is

    a subscript n equals a subscript n minus 1 end subscript plus 3.5

    Find the 12th term. -8, -5.5 , -3, -0.5, 2.0,....

    Maths-General
    • We have given a sequence -8, -5.5, -3, -0.5, 2.0,...
    • We have to find weather the given sequence is AP or not
    Step 1 of 1:
    We have given a sequence -8, -5.5, -3, -0.5, 2.0,...
    The given sequence is an AP
    And we know the recursive formula of any AP is a subscript n equals a subscript n minus 1 end subscript plus d.
    Where d is common difference.
    Here the common difference is 3.5.
    So, The recursive formula is

    a subscript n equals a subscript n minus 1 end subscript plus 3.5

    General
    Maths-

    Write an equation of a line that passes through the given line and is perpendicular to the given line.
    left parenthesis 4 comma 3 right parenthesis semicolon space 4 x minus 5 y equals 30

    • We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
    Step 1 of 1:
    We have to find a line passes through a point (4, 3) and perpendicular to a line 4x - 5y = 30
    Since product of two perpendicular lines is equal to -1.
    So,

    m cross times 4 over 5 equals negative 1

    m equals fraction numerator negative 5 over denominator 4 end fraction
    Therefore the equation of the line will be

    y minus 3 equals fraction numerator negative 5 over denominator 4 end fraction left parenthesis x minus 4 right parenthesis

    y equals fraction numerator negative 5 over denominator 4 end fraction x plus 8

    Write an equation of a line that passes through the given line and is perpendicular to the given line.
    left parenthesis 4 comma 3 right parenthesis semicolon space 4 x minus 5 y equals 30

    Maths-General
    • We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
    Step 1 of 1:
    We have to find a line passes through a point (4, 3) and perpendicular to a line 4x - 5y = 30
    Since product of two perpendicular lines is equal to -1.
    So,

    m cross times 4 over 5 equals negative 1

    m equals fraction numerator negative 5 over denominator 4 end fraction
    Therefore the equation of the line will be

    y minus 3 equals fraction numerator negative 5 over denominator 4 end fraction left parenthesis x minus 4 right parenthesis

    y equals fraction numerator negative 5 over denominator 4 end fraction x plus 8

    parallel

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