Question

which graph has a slope of \\(\frac{4}{5}\\)?

Explanation:

Step1: Recall slope formula

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

Step2: Analyze top graph

Points $(1,0)$ and $(5,-4)$. $m=\frac{-4-0}{5-1}=\frac{-4}{4}=-1$

Step3: Analyze middle graph

Points $(1,0)$ and $(5,-4)$. $m=\frac{-4-0}{5-1}=\frac{-4}{4}=-1$

Step4: Analyze bottom-right graph

Points $(-1,-2)$ and $(3,2)$. $m=\frac{2-(-2)}{3-(-1)}=\frac{4}{4}=1$

Step5: Analyze bottom-left graph

Points $(1,0)$ and $(5,4)$. $m=\frac{4-0}{5-1}=\frac{4}{5}$

Answer:

The bottom-left graph (the graph with red points at $(1,0)$ and $(5,4)$ that rises from left to right)