Question

Find the slope of the lines$l_1,l_2,l_3,$ and$l_4$in the below figure. (Lesson 1.10)

Short answer

The slope of the lines are$-2,\frac{1}{2},3,$ and $-\frac{1}{4}$.

Step-by-step solution

Step 1. Definition of the slope.

A slope is a measure of the steepness of a line.

$\begin{array}{l}\text{Slope}=\frac{\text{rise}}{\text{run}}\\ =\frac{\Delta y}{\Delta x}\end{array}$

Step 2. Find the slope of line l1.

Use the slope formula $m=\frac{\text{rise}}{\text{run}}$ to find the slope of $l_1$ that runs 2 units to the right and drops 4 units down from the point $\left(-1,2\right)$.

$\begin{array}{l}m=\frac{-4}{2}\\ =-2\end{array}$

Step 3. Find the slope of line l2.

Use the slope formula $m=\frac{\text{rise}}{\text{run}}$to find the slope of $l_2$that runs 2 units to the right and rises 1 unit up from the point (0,2).

$m=\frac{1}{2}$

Step 4. Find the slope of line l3.

Use the slope formula $m=\frac{\text{rise}}{\text{run}}$to find the slope of $l_3$that runs 1 unit to the right from the point (3,1).

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

Step 5. Find the slope of line l4.

Use the slope formula $m=\frac{\text{rise}}{\text{run}}$ to find the slope of $l_4$ that rises 1 unit up and runs 4 units to the left from the point $\left(-2,2\right)$.

$m=-\frac{1}{4}$