Find the Slope and y-intercept (-6,6) , (12,3)

$(- 6, 6)$ , $(12, 3)$

Step 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.

$m = \frac{3 - (6)}{12 - (- 6)}$

Simplify.

Reduce the expression by cancelling the common factors.

Cancel the common factor of $3 - (6)$ and $12 - (- 6)$ .

Rewrite $3$ as $- 1 (- 3)$ .

$m = \frac{- 1 \cdot - 3 - (6)}{12 - (- 6)}$

Factor $- 1$ out of $- 1 (- 3) - (6)$ .

$m = \frac{- 1 (- 3 + 6)}{12 - (- 6)}$

Reorder terms.

$m = \frac{- 1 (- 3 + 6)}{12 - 6 \cdot - 1}$

Factor $3$ out of $- 1 (- 3 + 6)$ .

$m = \frac{3 (- 1 (- 1 + 2))}{12 - 6 \cdot - 1}$

Cancel the common factors.

Factor $3$ out of $12$ .

$m = \frac{3 (- 1 (- 1 + 2))}{3 (4) - 6 \cdot - 1}$

Factor $3$ out of $- 6 \cdot - 1$ .

$m = \frac{3 (- 1 (- 1 + 2))}{3 (4) + 3 (- 2 \cdot - 1)}$

Factor $3$ out of $3 (4) + 3 (- 2 \cdot - 1)$ .

$m = \frac{3 (- 1 (- 1 + 2))}{3 (4 - 2 \cdot - 1)}$

Cancel the common factor.

$m = \frac{3 (- 1 (- 1 + 2))}{3 (4 - 2 \cdot - 1)}$

Rewrite the expression.

$m = \frac{- 1 (- 1 + 2)}{4 - 2 \cdot - 1}$

Add $- 1$ and $2$ .

$m = \frac{- 1 \cdot 1}{4 - 2 \cdot - 1}$

Simplify the denominator.

Multiply $- 2$ by $- 1$ .

$m = \frac{- 1 \cdot 1}{4 + 2}$

Add $4$ and $2$ .

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

Simplify the expression.

Multiply $- 1$ by $1$ .

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

Move the negative in front of the fraction.

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

Step 2

Find the value of the y-intercept.

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

$y = (- \frac{1}{6}) \cdot x + b$

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

$y = (- \frac{1}{6}) \cdot (- 6) + b$

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

$6 = (- \frac{1}{6}) \cdot (- 6) + b$

Rewrite the equation as $(- \frac{1}{6}) \cdot (- 6) + b = 6$ .

$(- \frac{1}{6}) \cdot (- 6) + b = 6$

Simplify each term.

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$\frac{- 1}{6} \cdot - 6 + b = 6$

Factor $6$ out of $- 6$ .

$\frac{- 1}{6} \cdot (6 (- 1)) + b = 6$

Cancel the common factor.

$\frac{- 1}{6} \cdot (6 \cdot - 1) + b = 6$

Rewrite the expression.

$- 1 \cdot - 1 + b = 6$

Multiply $- 1$ by $- 1$ .

$1 + b = 6$

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

Subtract $1$ from both sides of the equation.

$b = 6 - 1$

Subtract $1$ from $6$ .

$b = 5$

Step 3

List the slope and y-intercept.

Slope: $- \frac{1}{6}$

y-intercept: $(0, 5)$

Step 4

Find the Slope and y-intercept (-6,6) , (12,3)

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