So in the question we are given the points: (8,0) and (0,12)
In order to find the slope, we use the equation:
[tex] \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
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):
[tex] \frac{12-0}{0-8}=\frac{12}{-8}=-\frac{3}{2} [/tex]
So now we know the slope of the equation is [tex] -\frac{3}{2} [/tex].
The slope-intercept form of a line follows the form:
[tex] y=mx+b [/tex]
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:
[tex] y=-\frac{3}{2}x+12 [/tex]
