Find the Equation Using Point-Slope Formula (-4,-9) ; m=-3/4

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

Step 1

Use the slope $- \frac{3}{4}$ and a given point $(- 4, - 9)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 9) = - \frac{3}{4} \cdot (x - (- 4))$

Step 2

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

$y + 9 = - \frac{3}{4} \cdot (x + 4)$

Step 3

Solve for $y$ .

Simplify $- \frac{3}{4} \cdot (x + 4)$ .

Rewrite.

$y + 9 = 0 + 0 - \frac{3}{4} \cdot (x + 4)$

Simplify terms.

Apply the distributive property.

$y + 9 = - \frac{3}{4} x - \frac{3}{4} \cdot 4$

Combine $x$ and $\frac{3}{4}$ .

$y + 9 = - \frac{x \cdot 3}{4} - \frac{3}{4} \cdot 4$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$y + 9 = - \frac{x \cdot 3}{4} + \frac{- 3}{4} \cdot 4$

Cancel the common factor.

$y + 9 = - \frac{x \cdot 3}{4} + \frac{- 3}{4} \cdot 4$

Rewrite the expression.

$y + 9 = - \frac{x \cdot 3}{4} - 3$

Move $3$ to the left of $x$ .

$y + 9 = - \frac{3 x}{4} - 3$

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

Subtract $9$ from both sides of the equation.

$y = - \frac{3 x}{4} - 3 - 9$

Subtract $9$ from $- 3$ .

$y = - \frac{3 x}{4} - 12$

Write in $y = m x + b$ form.

Reorder terms.

$y = - (\frac{3}{4} x) - 12$

Remove parentheses.

$y = - \frac{3}{4} x - 12$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - \frac{3}{4} x - 12$

Point-slope form:

$y + 9 = - \frac{3}{4} \cdot (x + 4)$

Step 5

Find the Equation Using Point-Slope Formula (-4,-9) ; m=-3/4

Related Questions

Support LCMGCF.com by disabling your adblocker.