which linear function represents a slope of $\frac{1}{4}$?

Explanation:

Step1: Recall slope - formula

The slope formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Check first table

For the points $(3,-11)$ and $(6,1)$ from the first table, $m=\frac{1-(-11)}{6 - 3}=\frac{12}{3}=4$.

Step3: Check second graph

Let's take two points on the line in the second graph. Suppose the starting - point is $(0,3)$ and another point is $(4,4)$. Then $m=\frac{4 - 3}{4-0}=\frac{1}{4}$.

Step4: Check third table

For the points $(-5,32)$ and $(-1,24)$ from the third table, $m=\frac{24 - 32}{-1-(-5)}=\frac{-8}{4}=-2$.

Step5: Check fourth graph

Let's take two points on the line in the fourth graph. Suppose the points are $(2,0)$ and $(3,4)$. Then $m=\frac{4 - 0}{3 - 2}=4$.

Answer:

The second graph (the one with the line where taking two points gives a slope of $\frac{1}{4}$)