Write in Slope-Intercept Form (-12,4) and (0,2)

$(- 12, 4)$ and $(0, 2)$

Step 1

Find the slope of the line between $(- 12, 4)$ and $(0, 2)$ 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.

$m = \frac{2 - (4)}{0 - (- 12)}$

Simplify.

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2 - (4)$ and $0 - (- 12)$ .

Rewrite $2$ as $- 1 (- 2)$ .

$m = \frac{- 1 \cdot - 2 - (4)}{0 - (- 12)}$

Factor $- 1$ out of $- 1 (- 2) - (4)$ .

$m = \frac{- 1 (- 2 + 4)}{0 - (- 12)}$

Reorder terms.

$m = \frac{- 1 (- 2 + 4)}{0 - 12 \cdot - 1}$

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

$m = \frac{2 (- 1 (- 1 + 2))}{0 - 12 \cdot - 1}$

Cancel the common factors.

Factor $2$ out of $0$ .

$m = \frac{2 (- 1 (- 1 + 2))}{2 (0) - 12 \cdot - 1}$

Factor $2$ out of $- 12 \cdot - 1$ .

$m = \frac{2 (- 1 (- 1 + 2))}{2 (0) + 2 (- 6 \cdot - 1)}$

Factor $2$ out of $2 (0) + 2 (- 6 \cdot - 1)$ .

$m = \frac{2 (- 1 (- 1 + 2))}{2 (0 - 6 \cdot - 1)}$

Cancel the common factor.

$m = \frac{2 (- 1 (- 1 + 2))}{2 (0 - 6 \cdot - 1)}$

Rewrite the expression.

$m = \frac{- 1 (- 1 + 2)}{0 - 6 \cdot - 1}$

Add $- 1$ and $2$ .

$m = \frac{- 1 \cdot 1}{0 - 6 \cdot - 1}$

Simplify the denominator.

Multiply $- 6$ by $- 1$ .

$m = \frac{- 1 \cdot 1}{0 + 6}$

Add $0$ and $6$ .

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

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

Use the slope $- \frac{1}{6}$ and a given point $(- 12, 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (4) = - \frac{1}{6} \cdot (x - (- 12))$

Step 3

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

$y - 4 = - \frac{1}{6} \cdot (x + 12)$

Step 4

Write the equation in $y = m x + b$ form.

Solve for $y$ .

Simplify $- \frac{1}{6} \cdot (x + 12)$ .

Rewrite.

$y - 4 = 0 + 0 - \frac{1}{6} \cdot (x + 12)$

Simplify by adding zeros.

$y - 4 = - \frac{1}{6} \cdot (x + 12)$

Apply the distributive property.

$y - 4 = - \frac{1}{6} x - \frac{1}{6} \cdot 12$

Combine $x$ and $\frac{1}{6}$ .

$y - 4 = - \frac{x}{6} - \frac{1}{6} \cdot 12$

Cancel the common factor of $6$ .

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

$y - 4 = - \frac{x}{6} + \frac{- 1}{6} \cdot 12$

Factor $6$ out of $12$ .

$y - 4 = - \frac{x}{6} + \frac{- 1}{6} \cdot (6 (2))$

Cancel the common factor.

$y - 4 = - \frac{x}{6} + \frac{- 1}{6} \cdot (6 \cdot 2)$

Rewrite the expression.

$y - 4 = - \frac{x}{6} - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$y - 4 = - \frac{x}{6} - 2$

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

Add $4$ to both sides of the equation.

$y = - \frac{x}{6} - 2 + 4$

Add $- 2$ and $4$ .

$y = - \frac{x}{6} + 2$

Reorder terms.

$y = - (\frac{1}{6} x) + 2$

Remove parentheses.

$y = - \frac{1}{6} x + 2$

Step 5

Write in Slope-Intercept Form (-12,4) and (0,2)

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