Find the Slope (4,1) , (2,4)

$(4, 1)$ , $(2, 4)$

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.

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

Step 4

Simplify.

Simplify the numerator.

Multiply $- 1$ by $1$ .

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

Subtract $1$ from $4$ .

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

Simplify the denominator.

Multiply $- 1$ by $4$ .

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

Subtract $4$ from $2$ .

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

Move the negative in front of the fraction.

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

Step 5

Find the Slope (4,1) , (2,4)

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