Find the Equation Using Point-Slope Formula (0,-7) , (7,-2)

$(0, - 7)$ , $(7, - 2)$

Step 1

Find the slope of the line between $(0, - 7)$ and $(7, - 2)$ 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.

$m = \frac{- 2 - (- 7)}{7 - (0)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 7$ .

$m = \frac{- 2 + 7}{7 - (0)}$

Add $- 2$ and $7$ .

$m = \frac{5}{7 - (0)}$

Simplify the denominator.

Multiply $- 1$ by $0$ .

$m = \frac{5}{7 + 0}$

Add $7$ and $0$ .

$m = \frac{5}{7}$

Step 2

Use the slope $\frac{5}{7}$ and a given point $(0, - 7)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 7) = \frac{5}{7} \cdot (x - (0))$

Step 3

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

$y + 7 = \frac{5}{7} \cdot (x + 0)$

Step 4

Solve for $y$ .

Simplify $\frac{5}{7} \cdot (x + 0)$ .

Add $x$ and $0$ .

$y + 7 = \frac{5}{7} \cdot x$

Combine $\frac{5}{7}$ and $x$ .

$y + 7 = \frac{5 x}{7}$

Subtract $7$ from both sides of the equation.

$y = \frac{5 x}{7} - 7$

Step 5

Reorder terms.

$y = \frac{5}{7} x - 7$

Step 6

List the equation in different forms.

Slope-intercept form:

$y = \frac{5}{7} x - 7$

Point-slope form:

$y + 7 = \frac{5}{7} \cdot (x + 0)$

Step 7

Find the Equation Using Point-Slope Formula (0,-7) , (7,-2)

Related Questions

Support LCMGCF.com by disabling your adblocker.