Question

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

Explanation:

Step1: Recall slope formula

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

Step2: Select two - points on each graph

For each graph, pick two distinct points on the line. Let the points be $(x_1,y_1)$ and $(x_2,y_2)$.

Step3: Calculate the slope for each graph

For example, if for a graph the two points are $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(5,4)$, then $m=\frac{4 - 0}{5 - 0}=\frac{4}{5}$.

Answer:

The graph for which when two points are selected and the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ is applied gives a value of $\frac{4}{5}$. Without the ability to actually calculate the slopes of the given graphs here, the general process is as described above. You need to pick two points on each line of the given graphs and calculate the slope using the formula to find the graph with slope $\frac{4}{5}$.