Algebra Examples

$(- 3, - 4)$ , $(- 2, - 9)$

Find the value of the slope.

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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.

$m = \frac{- 9 - (- 4)}{- 2 - (- 3)}$

Simplify.

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Simplify the numerator.

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Multiply $- 1$ by $- 4$ .

$m = \frac{- 9 + 4}{- 2 - (- 3)}$

Add $- 9$ and $4$ .

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

Simplify the denominator.

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Remove parentheses.

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

Multiply $- 1$ by $- 3$ .

$m = \frac{- 5}{- 2 + 3}$

Add $- 2$ and $3$ .

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

Divide $- 5$ by $1$ .

$m = - 5$

Find the value of the y-intercept.

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Substitute the value of $m$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (- 5) \cdot x + b$

Substitute the value of $x$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (- 5) \cdot (- 3) + b$

Substitute the value of $y$ into the slope-intercept form of the equation, $y = m x + b$ .

$(- 4) = (- 5) \cdot (- 3) + b$

Rewrite the equation as $(- 5) \cdot (- 3) + b = - 4$ .

$(- 5) \cdot (- 3) + b = - 4$

Simplify each term.

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Multiply $- 5$ by $- 3$ .

$(- 5) (- 3) + b = - 4$

Multiply $- 5$ by $- 3$ .

$15 + b = - 4$

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

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Subtract $15$ from both sides of the equation.

$b = - 15 - 4$

Subtract $4$ from $- 15$ .

$b = - 19$

The values of the slope and y-intercept are $m = - 5$ and $b = - 19$

$m = - 5$

$b = - 19$

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