Find the Equation Using Point-Slope Formula (-6,-7) , (-18,-21)

$(- 6, - 7)$ , $(- 18, - 21)$

Step 1

Find the slope of the line between $(- 6, - 7)$ and $(- 18, - 21)$ 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.

$m = \frac{- 21 - (- 7)}{- 18 - (- 6)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 7$ .

$m = \frac{- 21 + 7}{- 18 - (- 6)}$

Add $- 21$ and $7$ .

$m = \frac{- 14}{- 18 - (- 6)}$

Simplify the denominator.

Multiply $- 1$ by $- 6$ .

$m = \frac{- 14}{- 18 + 6}$

Add $- 18$ and $6$ .

$m = \frac{- 14}{- 12}$

Cancel the common factor of $- 14$ and $- 12$ .

Factor $- 2$ out of $- 14$ .

$m = \frac{- 2 \cdot 7}{- 12}$

Cancel the common factors.

Factor $- 2$ out of $- 12$ .

$m = \frac{- 2 \cdot 7}{- 2 \cdot 6}$

Cancel the common factor.

$m = \frac{- 2 \cdot 7}{- 2 \cdot 6}$

Rewrite the expression.

$m = \frac{7}{6}$

Step 2

Use the slope $\frac{7}{6}$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

Step 3

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

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

Step 4

Solve for $y$ .

Simplify $\frac{7}{6} \cdot (x + 6)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Combine $\frac{7}{6}$ and $x$ .

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

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

$y + 7 = \frac{7 x}{6} + 7$

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

Subtract $7$ from both sides of the equation.

$y = \frac{7 x}{6} + 7 - 7$

Combine the opposite terms in $\frac{7 x}{6} + 7 - 7$ .

Subtract $7$ from $7$ .

$y = \frac{7 x}{6} + 0$

Add $\frac{7 x}{6}$ and $0$ .

$y = \frac{7 x}{6}$

Step 5

Reorder terms.

$y = \frac{7}{6} x$

Step 6

List the equation in different forms.

Slope-intercept form:

$y = \frac{7}{6} x$

Point-slope form:

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

Step 7

Find the Equation Using Point-Slope Formula (-6,-7) , (-18,-21)

Related Questions

Support LCMGCF.com by disabling your adblocker.