Find the Slope and y-intercept (-9,7) , (9,1)

$(- 9, 7)$ , $(9, 1)$

Find the value of the slope.

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.

$m = \frac{1 - (7)}{9 - (- 9)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $7$ .

$m = \frac{1 - 7}{9 - (- 9)}$

Subtract $7$ from $1$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 9$ .

$m = \frac{- 6}{9 + 9}$

Add $9$ and $9$ .

$m = \frac{- 6}{18}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 6$ and $18$ .

Factor $6$ out of $- 6$ .

$m = \frac{6 (- 1)}{18}$

Cancel the common factors.

Factor $6$ out of $18$ .

$m = \frac{6 \cdot - 1}{6 \cdot 3}$

Cancel the common factor.

$m = \frac{6 \cdot - 1}{6 \cdot 3}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Find the value of the y-intercept.

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

$y = (- \frac{1}{3}) \cdot x + b$

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

$y = (- \frac{1}{3}) \cdot (- 9) + b$

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

$7 = (- \frac{1}{3}) \cdot (- 9) + b$

Rewrite the equation as $(- \frac{1}{3}) \cdot (- 9) + b = 7$ .

$(- \frac{1}{3}) \cdot (- 9) + b = 7$

Simplify each term.

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{- 1}{3} \cdot - 9 + b = 7$

Factor $3$ out of $- 9$ .

$\frac{- 1}{3} \cdot (3 (- 3)) + b = 7$

Cancel the common factor.

$\frac{- 1}{3} \cdot (3 \cdot - 3) + b = 7$

Rewrite the expression.

$- 1 \cdot - 3 + b = 7$

Multiply $- 1$ by $- 3$ .

$3 + b = 7$

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

Subtract $3$ from both sides of the equation.

$b = 7 - 3$

Subtract $3$ from $7$ .

$b = 4$

List the slope and y-intercept.

Slope: $- \frac{1}{3}$

y-intercept: $(0, 4)$

Find the Slope and y-intercept (-9,7) , (9,1)

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