Find the Equation Using Point-Slope Formula (-10,-20) , (1,-9)

$(- 10, - 20)$ , $(1, - 9)$

Find the slope of the line between $(- 10, - 20)$ and $(1, - 9)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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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.

$m = \frac{- 9 - (- 20)}{1 - (- 10)}$

Simplify.

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Simplify the numerator.

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Multiply $- 1$ by $- 20$ .

$m = \frac{- 9 + 20}{1 - (- 10)}$

Add $- 9$ and $20$ .

$m = \frac{11}{1 - (- 10)}$

Simplify the denominator.

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Multiply $- 1$ by $- 10$ .

$m = \frac{11}{1 + 10}$

Add $1$ and $10$ .

$m = \frac{11}{11}$

Divide $11$ by $11$ .

$m = 1$

Use the slope $1$ and a given point $(- 10, - 20)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 20) = (1) (x - (- 10))$

Simplify the equation and keep it in point-slope form.

$y + 20 = 1 \cdot (x + 10)$

Solve for $y$ .

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Multiply $x + 10$ by $1$ .

$y + 20 = x + 10$

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

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Subtract $20$ from both sides of the equation.

$y = x + 10 - 20$

Subtract $20$ from $10$ .

$y = x - 10$

List the equation in different forms.

Slope-intercept form:

$y = x - 10$

Point-slope form:

$y + 20 = 1 \cdot (x + 10)$

Find the Equation Using Point-Slope Formula (-10,-20) , (1,-9)

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