Question
Find the value of the y-intercept in the equation 3x-y+5=0.
Hint:
The given equation is in the general form of equation of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. First we convert the given equation in this form by rearranging the terms. Further, compare the new equation with the standard form to get the y-intercept.
The correct answer is: y-intercept = 5
Step by step solution:
The given equation of the line is
3x - y + 5 = 0
We need to convert this equation in the slope-intercept form of the line, which is
y = mx + c
Rewriting the given equation, we have
-y = - 3x - 5
Dividing by (-1), we get
y = 3x + 5
Simplifying, we get
y = 3x + 5
Comparing the above equation with y = mx + c, we get
m = 3; c = 5
Thus, we get
y-intercept = 5
We need to convert this equation in the slope-intercept form of the line, which is
Rewriting the given equation, we have
Dividing by (-1), we get
Simplifying, we get
Comparing the above equation with y = mx + c, we get
Thus, we get
We can find the slope and y-intercept directly from the general form of the equation too; slope =
and y-intercept = 
, where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula.
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¶The standard form of a linear equation in one variable is: ax + b = 0
Where,
The letters 'a' and 'b' are real numbers.
'a' and 'b' are both greater than zero.
In an academic contest correct answers earn 12 points and incorrect answers lose 5
points. In the final round, school A starts with 165 points and gives the same number
of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
ii)How many answers did each school get correct in the final round?
A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable. As a result, this equation has only one solution, x = 5/2.
¶The standard form of a linear equation in one variable is: ax + b = 0
Where,
The letters 'a' and 'b' are real numbers.
'a' and 'b' are both greater than zero.
