Find the Slope of a Line Using Points on a Graph

The slope of a line is the ratio of the change in $y$ and the change in $x$. You can use the slope formula, $m=\frac{y_2-y_1}{x_2-x_1}$, to find the slope of the line through points $(x_1,y_1)$ and $(x_2,y_2)$.

Find the slope of the line that goes through points

1. $A$ and $D$
2. $A$ and $B$
3. $C$ and $D$

Here’s how to find the slope given two points.

a.

Step 1 - First, name $B(-3,-4)$ as point 1 and $D(4,3)$ as point 2.

$(x_1,y_1)$ and $(x_2,y_2)$

$(-3,-4)$ and $(4,3)$

Step 2 - Use the slope formula.

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

Step 3 - Substitute the values: $y_2=-3$, $y_1=3$, $x_2=-1$, $x_1=2$.

$m=\frac{-3-3}{-1-2}$

Step 4 - Simplify.

$m=\frac{-6}{-3}$

$m=2$

b.

Step 1 - First, name $A(2,3)$ as point 1 and $B(4,-1)$ as point 2.

$(x_1,y_1)$ and $(x_2,y_2)$

$(2,3)$ and $(4,-1)$

Step 2 - Use the slope formula.

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

Step 3 - Substitute the values: $y_2=-1$, $y_1=3$, $x_2=4$, $x_1=2$.

$m=\frac{-1-3}{4-2}$

Step 4 - Simplify.

$m=\frac{-4}{2}$

$m=-2$

c.

Step 1 - First, name $C(-2,5)$ as point 1 and $D(-1,-3)$ as point 2.

$(x_1,y_1)$ and $(x_2,y_2)$

$(-2,5)$ and $(-1,-3)$

Step 2 - Use the slope formula.

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

Step 3 - Substitute the values: $y_2=-3$, $y_1=5$, $x_2=-1$, $x_1=-2$.

$m=\frac{-3-5}{-1-(-2)}$

Step 4 - Simplify.

$m=\frac{-8}{1}$

$m=-8$

Videos: Finding the Slope of a Line

Khan Academy: Slope from a Graph

Watch this video to see how to find the slope from a graph.

Khan Academy: Slope from Two Points

Watch this video to see how to find the slope given two points.