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The equation for line $q$ can be written as $y= \frac{8}{3}x-1$ . Line $r$ is perpendicular to line $q$ and passes through $(8, -7)$ . What is the equation of line $r$ ? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

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Write an equation for a parallel or perpendicular line

Full solution

Q. The equation for line

q

can be written as

y= \frac{8}{3}x-1

. Line

r

is perpendicular to line

q

and passes through

(8, -7)

. What is the equation of line

r

? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Find Perpendicular Slope: Line $q$ has a slope of $\frac{8}{3}$ . Since line $r$ is perpendicular to line $q$ , its slope will be the negative reciprocal of $\frac{8}{3}$ .
Calculate Slope of Line $r$ : The negative reciprocal of $\frac{8}{3}$ is $-\frac{3}{8}$ . This is the slope of line $r$ .
Use Point-Slope Form: Using the point-slope form, $y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is the point $(8, -7)$ , we plug in the values to find the equation of line $r$ .
Simplify Equation: $y - (-7) = -\frac{3}{8}(x - 8)$
Simplify Equation: $y - (-7) = -\frac{3}{8}(x - 8)$ Simplify the equation to get $y + 7 = -\frac{3}{8}x + 3$

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