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Question

The line y equals negative 0.5 x plus b passes through the points left parenthesis 1 comma 5.5 right parenthesis comma left parenthesis 3 comma p right parenthesis comma left parenthesis 4 comma 4 right parenthesis comma text  and  end text left parenthesis 7 comma n right parenthesis .Find b, n, and p.

hintHint:

A linear equation in two variables is given by a x plus b y plus c equals 0. The slope of a line is: m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction and the slope intercept form of a line is:y equals m x plus c , where c is the y-intercept.
We are asked to find the values of b, n and p.

The correct answer is: Thus, the values of n=2.5,p=4.5&b=6.


    ANSWER:
    Step 1 of 1:
    To find the value of , substitute any of the points in the equation and solve them.
    y equals negative 0.5 x plus b
    4 equals negative 0.5 left parenthesis 4 right parenthesis plus b
    4 equals negative 2 plus b
    4 plus 2 equals b
    6 equals b
    Step 2 of 3:
    Substitute left parenthesis 3 comma p right parenthesis straight & left parenthesis 4 comma 4 right parenthesis in the equation to find slope. Thus, we have:
    m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction
    negative 0.5 equals fraction numerator 4 minus p over denominator 4 minus 3 end fraction
    negative 0.5 equals fraction numerator 4 minus p ∣ over denominator 1 end fraction
    negative 0.5 equals 4 minus p
    p equals 4 plus 0.5
    p equals 4.5
    Step 3 of 3:
    To find the value of n, substitutein  left parenthesis 7 comma n right parenthesis straight & left parenthesis 4 comma 4 right parenthesisthe equation of slope.
    m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction
    negative 0.5 equals fraction numerator 4 minus n over denominator 4 minus 7 end fraction
    negative 0.5 equals fraction numerator 4 minus n over denominator negative 3 end fraction
    negative 0.5 cross times negative 3 equals 4 minus n
    1.5 equals 4 minus n
    1.5 minus 4 equals negative n
    negative 2.5 equals negative n
    2.5 equals n
    Thus, the values of  n equals 2.5 comma p equals 4.5 straight & b equals 6

    The values of n and p could also be found using the slope-point form but the given method is much more efficient.

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