Find the Perpendicular Line The line contains (-3,4) and is perpendicular to 4x+7y=5

The line contains $(- 3, 4)$ and is perpendicular to $4 x + 7 y = 5$

Solve $4 x + 7 y = 5$ .

Subtract $4 x$ from both sides of the equation.

$7 y = 5 - 4 x$

Divide each term in $7 y = 5 - 4 x$ by $7$ and simplify.

Divide each term in $7 y = 5 - 4 x$ by $7$ .

$\frac{7 y}{7} = \frac{5}{7} + \frac{- 4 x}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{5}{7} + \frac{- 4 x}{7}$

Divide $y$ by $1$ .

$y = \frac{5}{7} + \frac{- 4 x}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{5}{7} - \frac{4 x}{7}$

Find the slope when $y = \frac{5}{7} - \frac{4 x}{7}$ .

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 $\frac{5}{7}$ and $- \frac{4 x}{7}$ .

$y = - \frac{4 x}{7} + \frac{5}{7}$

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

Reorder terms.

$y = - (\frac{4}{7} x) + \frac{5}{7}$

Remove parentheses.

$y = - \frac{4}{7} x + \frac{5}{7}$

Using the slope-intercept form, the slope is $- \frac{4}{7}$ .

$m = - \frac{4}{7}$

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

$m_{perpendicular} = - \frac{1}{- \frac{4}{7}}$

Simplify $- \frac{1}{- \frac{4}{7}}$ to find the slope of the perpendicular line.

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{4}{7}}$

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{4}{7}}$

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 (\frac{7}{4})$

Multiply $\frac{7}{4}$ by $1$ .

$m_{perpendicular} = \frac{7}{4}$

Multiply $- - \frac{7}{4}$ .

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{7}{4})$

Multiply $\frac{7}{4}$ by $1$ .

$m_{perpendicular} = \frac{7}{4}$

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

Use the slope $\frac{7}{4}$ and a given point $(- 3, 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (4) = \frac{7}{4} \cdot (x - (- 3))$

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

$y - 4 = \frac{7}{4} \cdot (x + 3)$

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

Solve for $y$ .

Simplify $\frac{7}{4} \cdot (x + 3)$ .

Rewrite.

$y - 4 = 0 + 0 + \frac{7}{4} \cdot (x + 3)$

Simplify by adding zeros.

$y - 4 = \frac{7}{4} \cdot (x + 3)$

Apply the distributive property.

$y - 4 = \frac{7}{4} x + \frac{7}{4} \cdot 3$

Combine $\frac{7}{4}$ and $x$ .

$y - 4 = \frac{7 x}{4} + \frac{7}{4} \cdot 3$

Multiply $\frac{7}{4} \cdot 3$ .

Combine $\frac{7}{4}$ and $3$ .

$y - 4 = \frac{7 x}{4} + \frac{7 \cdot 3}{4}$

Multiply $7$ by $3$ .

$y - 4 = \frac{7 x}{4} + \frac{21}{4}$

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

Add $4$ to both sides of the equation.

$y = \frac{7 x}{4} + \frac{21}{4} + 4$

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{7 x}{4} + \frac{21}{4} + 4 \cdot \frac{4}{4}$

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

$y = \frac{7 x}{4} + \frac{21}{4} + \frac{4 \cdot 4}{4}$

Combine the numerators over the common denominator.

$y = \frac{7 x}{4} + \frac{21 + 4 \cdot 4}{4}$

Simplify the numerator.

Multiply $4$ by $4$ .

$y = \frac{7 x}{4} + \frac{21 + 16}{4}$

Add $21$ and $16$ .

$y = \frac{7 x}{4} + \frac{37}{4}$

Reorder terms.

$y = \frac{7}{4} x + \frac{37}{4}$

Find the Perpendicular Line The line contains (-3,4) and is perpendicular to 4x+7y=5

Related Questions

Support LCMGCF.com by disabling your adblocker.