Write in Slope-Intercept Form (-12,14) and (6,-1)

$(- 12, 14)$ and $(6, - 1)$

Step 1

Find the slope of the line between $(- 12, 14)$ and $(6, - 1)$ 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.

$m = \frac{- 1 - (14)}{6 - (- 12)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $14$ .

$m = \frac{- 1 - 14}{6 - (- 12)}$

Subtract $14$ from $- 1$ .

$m = \frac{- 15}{6 - (- 12)}$

Simplify the denominator.

Multiply $- 1$ by $- 12$ .

$m = \frac{- 15}{6 + 12}$

Add $6$ and $12$ .

$m = \frac{- 15}{18}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 15$ and $18$ .

Factor $3$ out of $- 15$ .

$m = \frac{3 (- 5)}{18}$

Cancel the common factors.

Factor $3$ out of $18$ .

$m = \frac{3 \cdot - 5}{3 \cdot 6}$

Cancel the common factor.

$m = \frac{3 \cdot - 5}{3 \cdot 6}$

Rewrite the expression.

$m = \frac{- 5}{6}$

Move the negative in front of the fraction.

$m = - \frac{5}{6}$

Step 2

Use the slope $- \frac{5}{6}$ and a given point $(- 12, 14)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (14) = - \frac{5}{6} \cdot (x - (- 12))$

Step 3

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

$y - 14 = - \frac{5}{6} \cdot (x + 12)$

Step 4

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

Solve for $y$ .

Simplify $- \frac{5}{6} \cdot (x + 12)$ .

Rewrite.

$y - 14 = 0 + 0 - \frac{5}{6} \cdot (x + 12)$

Simplify terms.

Apply the distributive property.

$y - 14 = - \frac{5}{6} x - \frac{5}{6} \cdot 12$

Combine $x$ and $\frac{5}{6}$ .

$y - 14 = - \frac{x \cdot 5}{6} - \frac{5}{6} \cdot 12$

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$y - 14 = - \frac{x \cdot 5}{6} + \frac{- 5}{6} \cdot 12$

Factor $6$ out of $12$ .

$y - 14 = - \frac{x \cdot 5}{6} + \frac{- 5}{6} \cdot (6 (2))$

Cancel the common factor.

$y - 14 = - \frac{x \cdot 5}{6} + \frac{- 5}{6} \cdot (6 \cdot 2)$

Rewrite the expression.

$y - 14 = - \frac{x \cdot 5}{6} - 5 \cdot 2$

Multiply $- 5$ by $2$ .

$y - 14 = - \frac{x \cdot 5}{6} - 10$

Move $5$ to the left of $x$ .

$y - 14 = - \frac{5 x}{6} - 10$

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

Add $14$ to both sides of the equation.

$y = - \frac{5 x}{6} - 10 + 14$

Add $- 10$ and $14$ .

$y = - \frac{5 x}{6} + 4$

Reorder terms.

$y = - (\frac{5}{6} x) + 4$

Remove parentheses.

$y = - \frac{5}{6} x + 4$

Step 5

Write in Slope-Intercept Form (-12,14) and (6,-1)

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