Write in Slope-Intercept Form (9,-2) and (1,6)

$(9, - 2)$ and $(1, 6)$

Find the slope of the line between $(9, - 2)$ and $(1, 6)$ 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.

$m = \frac{6 - (- 2)}{1 - (9)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 2$ .

$m = \frac{6 + 2}{1 - (9)}$

Add $6$ and $2$ .

$m = \frac{8}{1 - (9)}$

Simplify the denominator.

Multiply $- 1$ by $9$ .

$m = \frac{8}{1 - 9}$

Subtract $9$ from $1$ .

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

Divide $8$ by $- 8$ .

$m = - 1$

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

$y - (- 2) = - 1 \cdot (x - (9))$

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

$y + 2 = - 1 \cdot (x - 9)$

Solve for $y$ .

Simplify $- 1 \cdot (x - 9)$ .

Rewrite.

$y + 2 = 0 + 0 - 1 \cdot (x - 9)$

Simplify by adding zeros.

$y + 2 = - 1 \cdot (x - 9)$

Apply the distributive property.

$y + 2 = - 1 x - 1 \cdot - 9$

Simplify the expression.

Rewrite $- 1 x$ as $- x$ .

$y + 2 = - x - 1 \cdot - 9$

Multiply $- 1$ by $- 9$ .

$y + 2 = - x + 9$

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

Subtract $2$ from both sides of the equation.

$y = - x + 9 - 2$

Subtract $2$ from $9$ .

$y = - x + 7$

Write in Slope-Intercept Form (9,-2) and (1,6)

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