Find the Equation Using Point-Slope Formula m=8/9 , (6,-3)

$m = \frac{8}{9}$ , $(6, - 3)$

Step 1

Use the slope $\frac{8}{9}$ and a given point $(6, - 3)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 3) = \frac{8}{9} \cdot (x - (6))$

Step 2

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

$y + 3 = \frac{8}{9} \cdot (x - 6)$

Step 3

Solve for $y$ .

Simplify $\frac{8}{9} \cdot (x - 6)$ .

Rewrite.

$y + 3 = 0 + 0 + \frac{8}{9} \cdot (x - 6)$

Simplify by adding zeros.

$y + 3 = \frac{8}{9} \cdot (x - 6)$

Apply the distributive property.

$y + 3 = \frac{8}{9} x + \frac{8}{9} \cdot - 6$

Combine $\frac{8}{9}$ and $x$ .

$y + 3 = \frac{8 x}{9} + \frac{8}{9} \cdot - 6$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$y + 3 = \frac{8 x}{9} + \frac{8}{3 (3)} \cdot - 6$

Factor $3$ out of $- 6$ .

$y + 3 = \frac{8 x}{9} + \frac{8}{3 \cdot 3} \cdot (3 \cdot - 2)$

Cancel the common factor.

$y + 3 = \frac{8 x}{9} + \frac{8}{3 \cdot 3} \cdot (3 \cdot - 2)$

Rewrite the expression.

$y + 3 = \frac{8 x}{9} + \frac{8}{3} \cdot - 2$

Combine $\frac{8}{3}$ and $- 2$ .

$y + 3 = \frac{8 x}{9} + \frac{8 \cdot - 2}{3}$

Simplify the expression.

Multiply $8$ by $- 2$ .

$y + 3 = \frac{8 x}{9} + \frac{- 16}{3}$

Move the negative in front of the fraction.

$y + 3 = \frac{8 x}{9} - \frac{16}{3}$

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

Subtract $3$ from both sides of the equation.

$y = \frac{8 x}{9} - \frac{16}{3} - 3$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{8 x}{9} - \frac{16}{3} - 3 \cdot \frac{3}{3}$

Combine $- 3$ and $\frac{3}{3}$ .

$y = \frac{8 x}{9} - \frac{16}{3} + \frac{- 3 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{8 x}{9} + \frac{- 16 - 3 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 3$ by $3$ .

$y = \frac{8 x}{9} + \frac{- 16 - 9}{3}$

Subtract $9$ from $- 16$ .

$y = \frac{8 x}{9} + \frac{- 25}{3}$

Move the negative in front of the fraction.

$y = \frac{8 x}{9} - \frac{25}{3}$

Reorder terms.

$y = \frac{8}{9} x - \frac{25}{3}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = \frac{8}{9} x - \frac{25}{3}$

Point-slope form:

$y + 3 = \frac{8}{9} \cdot (x - 6)$

Step 5

Find the Equation Using Point-Slope Formula m=8/9 , (6,-3)

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