Question

Write an equation in slope-intercept form for the line that satisfies the following condition. x-intercept 8, and y-intercept 12

Answer 1

So in the question we are given the points: (8,0) and (0,12)

In order to find the slope, we use the equation:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

where subscripts 1 and 2 can apply to either of the points as long as they remain consistent. Let's use subscript 1 for the point (8,0) and subscript 2 for the point (0,12):

$\frac{12-0}{0-8}=\frac{12}{-8}=-\frac{3}{2}$

So now we know the slope of the equation is $-\frac{3}{2}$.

The slope-intercept form of a line follows the form:

$y=mx+b$

where x and y are from a given point on the line, m is the slope of the line, and b is the y-intercept of the line.

So since we are told the y-intercept in the question, we can then plug in the numbers to the equation for the line:

$y=-\frac{3}{2}x+12$