Precalculus Examples

$(- 5, 3)$ and $(7, 9)$

Step 1

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

Step 2

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 3

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{9 - (3)}{7 - (- 5)}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Multiply $- 1$ by $3$ .

$m = \frac{9 - 3}{7 - (- 5)}$

Step 4.1.2

Subtract $3$ from $9$ .

$m = \frac{6}{7 - (- 5)}$

Step 4.2

Simplify the denominator.

Tap for more steps...

Step 4.2.1

Multiply $- 1$ by $- 5$ .

$m = \frac{6}{7 + 5}$

Step 4.2.2

Add $7$ and $5$ .

$m = \frac{6}{12}$

Step 4.3

Cancel the common factor of $6$ and $12$ .

Tap for more steps...

Step 4.3.1

Factor $6$ out of $6$ .

$m = \frac{6 (1)}{12}$

Step 4.3.2

Cancel the common factors.

Tap for more steps...

Step 4.3.2.1

Factor $6$ out of $12$ .

$m = \frac{6 \cdot 1}{6 \cdot 2}$

Step 4.3.2.2

Cancel the common factor.

$m = \frac{6 \cdot 1}{6 \cdot 2}$

Step 4.3.2.3

Rewrite the expression.

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

Step 5