Find the Perpendicular Line 3x-2y=-3 that contains the point (-5,5)

$3 x - 2 y = - 3$ that contains the point $(- 5, 5)$

Solve $3 x - 2 y = - 3$ .

Subtract $3 x$ from both sides of the equation.

$- 2 y = - 3 - 3 x$

Divide each term in $- 2 y = - 3 - 3 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 3 - 3 x$ by $- 2$ .

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

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

Dividing two negative values results in a positive value.

$y = \frac{3}{2} + \frac{3 x}{2}$

Find the slope when $y = \frac{3}{2} + \frac{3 x}{2}$ .

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Reorder $\frac{3}{2}$ and $\frac{3 x}{2}$ .

$y = \frac{3 x}{2} + \frac{3}{2}$

Reorder terms.

$y = \frac{3}{2} x + \frac{3}{2}$

Using the slope-intercept form, the slope is $\frac{3}{2}$ .

$m = \frac{3}{2}$

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{\frac{3}{2}}$

Simplify $- \frac{1}{\frac{3}{2}}$ to find the slope of the perpendicular line.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{2}{3}))$

Multiply $\frac{2}{3}$ by $1$ .

$m_{perpendicular} = - \frac{2}{3}$

Find the equation of the perpendicular line using the point-slope formula.

Use the slope $- \frac{2}{3}$ and a given point $(- 5, 5)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (5) = - \frac{2}{3} \cdot (x - (- 5))$

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

$y - 5 = - \frac{2}{3} \cdot (x + 5)$

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

Solve for $y$ .

Simplify $- \frac{2}{3} \cdot (x + 5)$ .

Rewrite.

$y - 5 = 0 + 0 - \frac{2}{3} \cdot (x + 5)$

Simplify by adding zeros.

$y - 5 = - \frac{2}{3} \cdot (x + 5)$

Apply the distributive property.

$y - 5 = - \frac{2}{3} x - \frac{2}{3} \cdot 5$

Combine $x$ and $\frac{2}{3}$ .

$y - 5 = - \frac{x \cdot 2}{3} - \frac{2}{3} \cdot 5$

Multiply $- \frac{2}{3} \cdot 5$ .

Multiply $5$ by $- 1$ .

$y - 5 = - \frac{x \cdot 2}{3} - 5 (\frac{2}{3})$

Combine $- 5$ and $\frac{2}{3}$ .

$y - 5 = - \frac{x \cdot 2}{3} + \frac{- 5 \cdot 2}{3}$

Multiply $- 5$ by $2$ .

$y - 5 = - \frac{x \cdot 2}{3} + \frac{- 10}{3}$

Simplify each term.

Move $2$ to the left of $x$ .

$y - 5 = - \frac{2 \cdot x}{3} + \frac{- 10}{3}$

Move the negative in front of the fraction.

$y - 5 = - \frac{2 x}{3} - \frac{10}{3}$

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

Add $5$ to both sides of the equation.

$y = - \frac{2 x}{3} - \frac{10}{3} + 5$

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{2 x}{3} - \frac{10}{3} + 5 \cdot \frac{3}{3}$

Combine $5$ and $\frac{3}{3}$ .

$y = - \frac{2 x}{3} - \frac{10}{3} + \frac{5 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = - \frac{2 x}{3} + \frac{- 10 + 5 \cdot 3}{3}$

Simplify the numerator.

Multiply $5$ by $3$ .

$y = - \frac{2 x}{3} + \frac{- 10 + 15}{3}$

Add $- 10$ and $15$ .

$y = - \frac{2 x}{3} + \frac{5}{3}$

Reorder terms.

$y = - (\frac{2}{3} x) + \frac{5}{3}$

Remove parentheses.

$y = - \frac{2}{3} x + \frac{5}{3}$

Find the Perpendicular Line 3x-2y=-3 that contains the point (-5,5)

Related Questions

Support LCMGCF.com by disabling your adblocker.