Find the Equation Using Point-Slope Formula (7,20) , (-2,11)

$(7, 20)$ , $(- 2, 11)$

Step 1

Find the slope of the line between $(7, 20)$ and $(- 2, 11)$ 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.

$m = \frac{11 - (20)}{- 2 - (7)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $20$ .

$m = \frac{11 - 20}{- 2 - (7)}$

Subtract $20$ from $11$ .

$m = \frac{- 9}{- 2 - (7)}$

Simplify the denominator.

Multiply $- 1$ by $7$ .

$m = \frac{- 9}{- 2 - 7}$

Subtract $7$ from $- 2$ .

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

Divide $- 9$ by $- 9$ .

$m = 1$

Step 2

Use the slope $1$ and a given point $(7, 20)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (20) = 1 \cdot (x - (7))$

Step 3

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

$y - 20 = 1 \cdot (x - 7)$

Step 4

Solve for $y$ .

Multiply $x - 7$ by $1$ .

$y - 20 = x - 7$

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

Add $20$ to both sides of the equation.

$y = x - 7 + 20$

Add $- 7$ and $20$ .

$y = x + 13$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = x + 13$

Point-slope form:

$y - 20 = 1 \cdot (x - 7)$

Step 6

Find the Equation Using Point-Slope Formula (7,20) , (-2,11)

Related Questions

Support LCMGCF.com by disabling your adblocker.