Question

which equation is a line that passes through the point (-4, -4) and has a y-intercept of 2? desmos graphing calculator new! classic version (image of desmos graphing interface) a. $y = \frac{2}{3}x + 2$ b. $y = \frac{3}{2}x + 2$ c. $y = 2x + 4$ d. $y = 2x + 12$

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a line is $y = mx + b$, where $b$ is the y - intercept. We know that $b = 2$, so the equation of the line should be in the form $y=mx + 2$. So we can eliminate option C ($y = 2x+4$, $b = 4$) and option D ($y=2x + 12$, $b = 12$) since their y - intercepts are not 2.

Step2: Test the point $(-4,-4)$ in remaining options

We have two remaining options: A: $y=\frac{2}{3}x + 2$ and B: $y=\frac{3}{2}x+2$.
For option A: Substitute $x=-4$ into $y=\frac{2}{3}x + 2$. Then $y=\frac{2}{3}\times(-4)+2=\frac{-8}{3}+2=\frac{-8 + 6}{3}=\frac{-2}{3}
eq - 4$.
For option B: Substitute $x = - 4$ into $y=\frac{3}{2}x+2$. Then $y=\frac{3}{2}\times(-4)+2=-6 + 2=-4$, which matches the given point $(-4,-4)$.

Answer:

B. $y=\frac{3}{2}x + 2$