Q14. - Algebra 1

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 $\frac{2}{5}$

Step-by-Step Solution

Answer

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

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" style="max-width: none; vertical-align: -4px;" $\left(-2,3\right)$.

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.