Q3. - Algebra 1

Question

What is the slope of the linear function graphed below?

A. $\frac{\text{-1}}{\text{3}}$

B. $\frac{\text{1}}{\text{2}}$

C. $\frac{\text{2}}{\text{3}}$

D. $\frac{\text{3}}{\text{2}}$

Step-by-Step Solution

Answer

The slope of the linear function is Option C. $\frac{\text{2}}{\text{3}}$.

Step 1. State the concept of slope of the line joining two points.

The slope $\left(m\right)$ of the line joining two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given as $m=\frac{y_2-y_1}{x_2-x_1}$.

Step 2. Find two points on the line.

From the graph, it can be seen that the line passes through the point $\left(3,1\right)$ and the y-intercept $\left(0,-1\right)$.

Step 3. Calculate the slope ( m ).

Substitute the point $\left(3,1\right)$ as $\left(x_1,y_1\right)$ and point $\left(0,-1\right)$ as $\left(x_2,y_2\right)$ in the formula of slope to find the slope.

$$\begin{gathered} \text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-1-1}{0-3} \\ =\frac{-2}{-3} \\ =\frac{2}{3} \end{gathered}$$

Thus, the slope of the graphed linear function is $\frac{2}{3}$.

Hence, option C is correct.