Question

What is the y-intercept of the line with a slope of −1/4 that passes through the point (−2,−9/2)?

Answer 1

The slope-point form of a line:

$y-y_0=m(x-x_0)$

We have

$m=-\dfrac{1}{4}\\\\\left(-2,\ -\dfrac{9}{2}\right)\to x=-2,\ y=-\dfrac{9}{2}$

Substitute

$y-\left(-\dfrac{9}{2}\right)=-\dfrac{1}{4}(x-(-2))\\\\y+\dfrac{9}{2}=-\dfrac{1}{4}(x+2)$

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

Solve for y:

$y+\dfrac{9}{2}=-\dfrac{1}{4}(x+2)\qquad|\text{use distributive property}\\\\y+\dfrac{9}{2}=-\dfrac{1}{4}x-\dfrac{1}{2}\qquad|\text{subtract}\ \dfrac{9}{2}\ \text{from both sides}\\\\y=-\dfrac{1}{4}x-\dfrac{10}{2}\\\\y=-\dfrac{1}{4}x-5$

Amswer: y-intercept = -5.