Question

match the linear equation to its graph. be sure to show work to prove your answer choice!

1. ( y = -\frac{2}{3}x )
2. ( y = \frac{1}{2}x - 5 )
3. ( y = 2x - 1 )
4. ( x = 4 )

a. graph of a line with positive slope
b. graph of a vertical line ( x = 4 )
c. graph of a line with steeper positive slope
d. graph of a line with negative slope

Explanation:

Step1: Analyze $y=-\frac{2}{3}x$

This is a linear equation in slope-intercept form $y=mx+b$, where slope $m=-\frac{2}{3}$ (negative, line falls left to right) and y-intercept $b=0$ (crosses origin $(0,0)$). Graph D has a negative slope and passes through the origin.

Step2: Analyze $y=\frac{1}{2}x-5$

Slope $m=\frac{1}{2}$ (positive, line rises left to right), y-intercept $b=-5$ (crosses y-axis at $(0,-5)$). Graph A has a gentle positive slope and low y-intercept.

Step3: Analyze $y=2x-1$

Slope $m=2$ (steep positive slope), y-intercept $b=-1$ (crosses y-axis at $(0,-1)$). Graph C has a steep positive slope and low y-intercept.

Step4: Analyze $x=4$

This is a vertical line where all points have $x=4$. Graph B is a vertical line.

Answer:

1. $y=-\frac{2}{3}x$: D
2. $y=\frac{1}{2}x-5$: A
3. $y=2x-1$: C
4. $x=4$: B