Question

Which is the slope of the linear function shown in the graph?

A$-\frac{5}{2}$

B$-\frac{2}{5}$

C$\frac{5}{2}$

D$\frac{2}{5}$

Short answer

The slope of the linear function shown in the graph is$-\frac{2}{5}$. Therefore the option B is correct.

Step-by-step solution

Step 1. Write the formula to find the slope of the line that passes through two points.

The slope of the line (m) that passes through the two points$\left(x_1,y_1\right)$ and$\left(x_2,y_2\right)$ is:

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

Step 2. Find the slope of the linear function shown in the graph.

From the given graph, it can be noticed that the graph of the linear function is a line passing through the points$\left(3,1\right)$ and width="47" height="20" role="math">−2,3.

The slope of the line (m) that passes through the points$\left(x_1,y_1\right)=\left(3,1\right)$ and$\left(x_2,y_2\right)=\left(-2,3\right)$ is:

$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{3-1}{-2-3} \\ =\frac{2}{-5} \\ =-\frac{2}{5} \end{gathered}$$

The slope of the linear function shown in the graph is$-\frac{2}{5}$. Therefore, the option B is correct.