Precalculus Examples

$(0, 0)$ , $(- 6, 6)$

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.

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

Finding the slope $m$ .

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Simplify the numerator.

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Multiply $- 1$ by $0$ .

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

Add $6$ and $0$ .

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

Simplify the denominator.

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Multiply $- 1$ by $0$ .

$m = \frac{6}{- 6 + 0}$

Add $- 6$ and $0$ .

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

Divide $6$ by $- 6$ .

$m = - 1$

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.

$y = (- 1) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- 1) \cdot (0) + b$

Substitute the value of $y$ into the equation.

$0 = (- 1) \cdot (0) + b$

Find the value of $b$ .

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Rewrite the equation as $(- 1) \cdot (0) + b = 0$ .

$(- 1) \cdot (0) + b = 0$

Simplify the left side.

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Simplify each term.

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Multiply $- 1$ by $0$ .

$(- 1) (0) + b = 0$

Multiply $- 1$ by $0$ .

$0 + b = 0$

Add $0$ and $b$ .

$b = 0$

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.

$y = - x$

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