Precalculus Examples

$(0, 9)$ , $(8, 6)$

Use $y = m x + b$ to calculate the equation of the line, where $m$ represents the slope and $b$ represents the y-intercept.

To calculate the equation of the line, use the $y = m x + b$ format.

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

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

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).

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

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

$m = \frac{6 - (9)}{8 - (0)}$

Finding the slope $m$ .

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Simplify the numerator.

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Multiply $- 1$ by $9$ .

$m = \frac{6 - 9}{8 - (0)}$

Subtract $9$ from $6$ .

$m = \frac{- 3}{8 - (0)}$

Simplify the denominator.

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Multiply $- 1$ by $0$ .

$m = \frac{- 3}{8 + 0}$

Add $8$ and $0$ .

$m = \frac{- 3}{8}$

Move the negative in front of the fraction.

$m = - \frac{3}{8}$

Find the value of $b$ using the formula for the equation of a line.

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Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

$y = (- \frac{3}{8}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{3}{8}) \cdot (0) + b$

Substitute the value of $y$ into the equation.

$9 = (- \frac{3}{8}) \cdot (0) + b$

Find the value of $b$ .

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Rewrite the equation as $(- \frac{3}{8}) \cdot (0) + b = 9$ .

$(- \frac{3}{8}) \cdot (0) + b = 9$

Simplify the left side.

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Multiply $(- \frac{3}{8}) (0)$ .

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Multiply $0$ by $- 1$ .

$0 (\frac{3}{8}) + b = 9$

Multiply $0$ by $\frac{3}{8}$ .

$0 + b = 9$

Add $0$ and $b$ .

$b = 9$

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = - \frac{3}{8} x + 9$

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