Find the Equation Using Point-Slope Formula (11,-9) , (12,18)

$(11, - 9)$ , $(12, 18)$

Step 1

Find the slope of the line between $(11, - 9)$ and $(12, 18)$ 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.

$m = \frac{18 - (- 9)}{12 - (11)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 9$ .

$m = \frac{18 + 9}{12 - (11)}$

Add $18$ and $9$ .

$m = \frac{27}{12 - (11)}$

Simplify the denominator.

Multiply $- 1$ by $11$ .

$m = \frac{27}{12 - 11}$

Subtract $11$ from $12$ .

$m = \frac{27}{1}$

Divide $27$ by $1$ .

$m = 27$

Step 2

Use the slope $27$ and a given point $(11, - 9)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 9) = 27 \cdot (x - (11))$

Step 3

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

$y + 9 = 27 \cdot (x - 11)$

Step 4

Solve for $y$ .

Simplify $27 \cdot (x - 11)$ .

Rewrite.

$y + 9 = 0 + 0 + 27 \cdot (x - 11)$

Simplify by adding zeros.

$y + 9 = 27 \cdot (x - 11)$

Apply the distributive property.

$y + 9 = 27 x + 27 \cdot - 11$

Multiply $27$ by $- 11$ .

$y + 9 = 27 x - 297$

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

Subtract $9$ from both sides of the equation.

$y = 27 x - 297 - 9$

Subtract $9$ from $- 297$ .

$y = 27 x - 306$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = 27 x - 306$

Point-slope form:

$y + 9 = 27 \cdot (x - 11)$

Step 6

Find the Equation Using Point-Slope Formula (11,-9) , (12,18)

Related Questions

Support LCMGCF.com by disabling your adblocker.