Question

Find the slope of the line through P and Q.(Lesson 1.10)

$P\left(0,0\right)\mathrm{and}Q\left(3,-1\right)$

Short answer

The slope of the line through P and Q is $-\frac{1}{3}$.

Step-by-step solution

Step 1. Apply the slope formula.

The slope of the line is $m=\frac{y_2-y_1}{x_2-x_1}$,Where$\left(x_1,y_1\right),\left(x_2,y_2\right)$ are coordinates of points lie on the line.

Step 2. Substitute the values in the slope formula.

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

Step 3. Calculate the slope.

$\begin{array}{l}m=\frac{-1-0}{3-0}\\ m=-\frac{1}{3}\end{array}$

Hence, the slope is $-\frac{1}{3}$.