Precalculus Examples

$(1, - 2)$ , $(3, 6)$

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.

$m = \frac{6 - (- 2)}{3 - (1)}$

Finding the slope $m$ .

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Simplify the numerator.

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Multiply $- 1$ by $- 2$ .

$m = \frac{6 + 2}{3 - (1)}$

Add $6$ and $2$ .

$m = \frac{8}{3 - (1)}$

Simplify the denominator.

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Remove parentheses.

$m = \frac{8}{3 - (1)}$

Multiply $- 1$ by $1$ .

$m = \frac{8}{3 - 1}$

Subtract $1$ from $3$ .

$m = \frac{8}{2}$

Divide $8$ by $2$ .

$m = 4$

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.

$y = (4) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (4) \cdot (1) + b$

Substitute the value of $y$ into the equation.

$(- 2) = (4) \cdot (1) + b$

Find the value of $b$ .

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Rewrite the equation as $(4) \cdot (1) + b = - 2$ .

$(4) \cdot (1) + b = - 2$

Simplify each term.

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Multiply $4$ by $1$ .

$(4) (1) + b = - 2$

Multiply $4$ by $1$ .

$4 + b = - 2$

Move all terms not containing $b$ to the right side of the equation.

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Subtract $4$ from both sides of the equation.

$b = - 4 - 2$

Subtract $2$ from $- 4$ .

$b = - 6$

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.

$y = 4 x - 6$

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