Calculus Examples

$f (2) = 4$ , $g (5) = 3$

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.

$m = \frac{3 - (4)}{5 - (2)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $4$ .

$m = \frac{3 - 4}{5 - (2)}$

Step 4.1.2

Subtract $4$ from $3$ .

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

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $2$ .

$m = \frac{- 1}{5 - 2}$

Step 4.2.2

Subtract $2$ from $5$ .

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

Step 4.3

Move the negative in front of the fraction.

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

Step 5