Find the Equation Using Point-Slope Formula (-9,9) and (8,-2)

$(- 9, 9)$ and $(8, - 2)$

Step 1

Find the slope of the line between $(- 9, 9)$ and $(8, - 2)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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.

$m = \frac{- 2 - (9)}{8 - (- 9)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $9$ .

$m = \frac{- 2 - 9}{8 - (- 9)}$

Subtract $9$ from $- 2$ .

$m = \frac{- 11}{8 - (- 9)}$

Simplify the denominator.

Multiply $- 1$ by $- 9$ .

$m = \frac{- 11}{8 + 9}$

Add $8$ and $9$ .

$m = \frac{- 11}{17}$

Move the negative in front of the fraction.

$m = - \frac{11}{17}$

Step 2

Use the slope $- \frac{11}{17}$ and a given point $(- 9, 9)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (9) = - \frac{11}{17} \cdot (x - (- 9))$

Step 3

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

$y - 9 = - \frac{11}{17} \cdot (x + 9)$

Step 4

Solve for $y$ .

Simplify $- \frac{11}{17} \cdot (x + 9)$ .

Rewrite.

$y - 9 = 0 + 0 - \frac{11}{17} \cdot (x + 9)$

Simplify by adding zeros.

$y - 9 = - \frac{11}{17} \cdot (x + 9)$

Apply the distributive property.

$y - 9 = - \frac{11}{17} x - \frac{11}{17} \cdot 9$

Combine $x$ and $\frac{11}{17}$ .

$y - 9 = - \frac{x \cdot 11}{17} - \frac{11}{17} \cdot 9$

Multiply $- \frac{11}{17} \cdot 9$ .

Multiply $9$ by $- 1$ .

$y - 9 = - \frac{x \cdot 11}{17} - 9 (\frac{11}{17})$

Combine $- 9$ and $\frac{11}{17}$ .

$y - 9 = - \frac{x \cdot 11}{17} + \frac{- 9 \cdot 11}{17}$

Multiply $- 9$ by $11$ .

$y - 9 = - \frac{x \cdot 11}{17} + \frac{- 99}{17}$

Simplify each term.

Move $11$ to the left of $x$ .

$y - 9 = - \frac{11 \cdot x}{17} + \frac{- 99}{17}$

Move the negative in front of the fraction.

$y - 9 = - \frac{11 x}{17} - \frac{99}{17}$

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

Add $9$ to both sides of the equation.

$y = - \frac{11 x}{17} - \frac{99}{17} + 9$

To write $9$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$y = - \frac{11 x}{17} - \frac{99}{17} + 9 \cdot \frac{17}{17}$

Combine $9$ and $\frac{17}{17}$ .

$y = - \frac{11 x}{17} - \frac{99}{17} + \frac{9 \cdot 17}{17}$

Combine the numerators over the common denominator.

$y = - \frac{11 x}{17} + \frac{- 99 + 9 \cdot 17}{17}$

Simplify the numerator.

Multiply $9$ by $17$ .

$y = - \frac{11 x}{17} + \frac{- 99 + 153}{17}$

Add $- 99$ and $153$ .

$y = - \frac{11 x}{17} + \frac{54}{17}$

Step 5

Reorder terms.

$y = - (\frac{11}{17} x) + \frac{54}{17}$

Step 6

Remove parentheses.

$y = - \frac{11}{17} x + \frac{54}{17}$

Step 7

List the equation in different forms.

Slope-intercept form:

$y = - \frac{11}{17} x + \frac{54}{17}$

Point-slope form:

$y - 9 = - \frac{11}{17} \cdot (x + 9)$

Step 8

Find the Equation Using Point-Slope Formula (-9,9) and (8,-2)

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