Examples

(1, 2)

$(1, 2)$ ,

(3, 4)

$(3, 4)$

Step 1

Slope is equal to the change in

y

$y$ over the change in

x

$x$ , or rise over run.

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

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

Step 2

The change in

x

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

y

$y$ is equal to the difference in y-coordinates (also called rise).

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

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

Step 3

Substitute in the values of

x

$x$ and

y

$y$ into the equation to find the slope.

m = \frac{4 - (2)}{3 - (1)}

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

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply

- 1

$- 1$ by

2

$2$ .

m = \frac{4 - 2}{3 - (1)}

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

Step 4.1.2

Subtract

2

$2$ from

4

$4$ .

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

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

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

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

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply

- 1

$- 1$ by

1

$1$ .

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

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

Step 4.2.2

Subtract

1

$1$ from

3

$3$ .

m = \frac{2}{2}

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

m = \frac{2}{2}

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

Step 4.3

Divide

2

$2$ by

2

$2$ .

m = 1

$m = 1$

m = 1

$m = 1$

Step 5

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