Question

1. which graph has a slope of one half.

Explanation:

Step1: Recall slope formula

Slope $m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

Step2: Analyze Graph 1

Pick points $(-4,2)$ and $(0,0)$: $m=\frac{0-2}{0-(-4)}=\frac{-2}{4}=-\frac{1}{2}$

Step3: Analyze Graph 2

Pick points $(0,2)$ and $(1,4)$: $m=\frac{4-2}{1-0}=2$

Step4: Analyze Graph 3

Pick points $(0,3)$ and $(2,-1)$: $m=\frac{-1-3}{2-0}=\frac{-4}{2}=-2$

Step5: Analyze Graph 4

Pick points $(0,-1)$ and $(4,0)$: $m=\frac{0-(-1)}{4-0}=\frac{1}{4}$
Wait correction: Pick points $(-4,-2)$ and $(4,0)$: $m=\frac{0-(-2)}{4-(-4)}=\frac{2}{8}=\frac{1}{4}$
Wait correction: Pick points $(2,0)$ and $(4,1)$: $m=\frac{1-0}{4-2}=\frac{1}{2}$

Answer:

The fourth graph (rightmost one) has a slope of $\frac{1}{2}$.