Find the Equation Using Point-Slope Formula (3,9) , (4,12)

$(3, 9)$ , $(4, 12)$

Step 1

Find the slope of the line between $(3, 9)$ and $(4, 12)$ 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.

$m = \frac{12 - (9)}{4 - (3)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $9$ .

$m = \frac{12 - 9}{4 - (3)}$

Subtract $9$ from $12$ .

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

Simplify the denominator.

Multiply $- 1$ by $3$ .

$m = \frac{3}{4 - 3}$

Subtract $3$ from $4$ .

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

Divide $3$ by $1$ .

$m = 3$

Step 2

Use the slope $3$ and a given point $(3, 9)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (9) = 3 \cdot (x - (3))$

Step 3

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

$y - 9 = 3 \cdot (x - 3)$

Step 4

Solve for $y$ .

Simplify $3 \cdot (x - 3)$ .

Rewrite.

$y - 9 = 0 + 0 + 3 \cdot (x - 3)$

Simplify by adding zeros.

$y - 9 = 3 \cdot (x - 3)$

Apply the distributive property.

$y - 9 = 3 x + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$y - 9 = 3 x - 9$

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

Add $9$ to both sides of the equation.

$y = 3 x - 9 + 9$

Combine the opposite terms in $3 x - 9 + 9$ .

Add $- 9$ and $9$ .

$y = 3 x + 0$

Add $3 x$ and $0$ .

$y = 3 x$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = 3 x$

Point-slope form:

$y - 9 = 3 \cdot (x - 3)$

Step 6

Find the Equation Using Point-Slope Formula (3,9) , (4,12)

Related Questions

Support LCMGCF.com by disabling your adblocker.