Write in Slope-Intercept Form (-6,-7) and (3,-4)

$(- 6, - 7)$ and $(3, - 4)$

Find the slope of the line between $(- 6, - 7)$ and $(3, - 4)$ 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.

$m = \frac{- 4 - (- 7)}{3 - (- 6)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 7$ .

$m = \frac{- 4 + 7}{3 - (- 6)}$

Add $- 4$ and $7$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 6$ .

$m = \frac{3}{3 + 6}$

Add $3$ and $6$ .

$m = \frac{3}{9}$

Cancel the common factor of $3$ and $9$ .

Factor $3$ out of $3$ .

$m = \frac{3 (1)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Use the slope $\frac{1}{3}$ and a given point $(- 6, - 7)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 7) = \frac{1}{3} \cdot (x - (- 6))$

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

$y + 7 = \frac{1}{3} \cdot (x + 6)$

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

Solve for $y$ .

Simplify $\frac{1}{3} \cdot (x + 6)$ .

Rewrite.

$y + 7 = 0 + 0 + \frac{1}{3} \cdot (x + 6)$

Simplify by adding zeros.

$y + 7 = \frac{1}{3} \cdot (x + 6)$

Apply the distributive property.

$y + 7 = \frac{1}{3} x + \frac{1}{3} \cdot 6$

Combine $\frac{1}{3}$ and $x$ .

$y + 7 = \frac{x}{3} + \frac{1}{3} \cdot 6$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$y + 7 = \frac{x}{3} + \frac{1}{3} \cdot (3 (2))$

Cancel the common factor.

$y + 7 = \frac{x}{3} + \frac{1}{3} \cdot (3 \cdot 2)$

Rewrite the expression.

$y + 7 = \frac{x}{3} + 2$

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

Subtract $7$ from both sides of the equation.

$y = \frac{x}{3} + 2 - 7$

Subtract $7$ from $2$ .

$y = \frac{x}{3} - 5$

Reorder terms.

$y = \frac{1}{3} x - 5$

Write in Slope-Intercept Form (-6,-7) and (3,-4)

Related Questions

Support LCMGCF.com by disabling your adblocker.