Write in Slope-Intercept Form (-6,-4) and (12,11)

$(- 6, - 4)$ and $(12, 11)$

Step 1

Find the slope of the line between $(- 6, - 4)$ and $(12, 11)$ 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.

$m = \frac{11 - (- 4)}{12 - (- 6)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 4$ .

$m = \frac{11 + 4}{12 - (- 6)}$

Add $11$ and $4$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 6$ .

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

Add $12$ and $6$ .

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

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.

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

Step 2

Use the slope $\frac{5}{6}$ and a given point $(- 6, - 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

Step 3

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

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

Step 4

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

Solve for $y$ .

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

Rewrite.

$y + 4 = 0 + 0 + \frac{5}{6} \cdot (x + 6)$

Simplify by adding zeros.

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

Apply the distributive property.

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

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

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

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

Subtract $4$ from both sides of the equation.

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

Subtract $4$ from $5$ .

$y = \frac{5 x}{6} + 1$

Reorder terms.

$y = \frac{5}{6} x + 1$

Step 5

Write in Slope-Intercept Form (-6,-4) and (12,11)

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