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The equation for line $p$ can be written as $y= \frac{9}{7}x-9$ . Line $q$ is perpendicular to line $p$ and passes through $(9, -6)$ . What is the equation of line $q$ ? 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

p

can be written as

y= \frac{9}{7}x-9

. Line

q

is perpendicular to line

p

and passes through

(9, -6)

. What is the equation of line

q

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

Line p's Equation: Line p's equation is $y = \frac{9}{7}x - 9$ . The slope of line p is $\frac{9}{7}$ .
Perpendicular Line Slope: Line $q$ is perpendicular to line $p$ , so its slope is the negative reciprocal of $\frac{9}{7}$ , which is $-\frac{7}{9}$ .
Calculate Y-Intercept: Using the point $(9, -6)$ and the slope $-\frac{7}{9}$ , plug into $y = mx + b$ to find $b$ , the y-intercept of line $q$ . $\newline$ $-6 = \left(-\frac{7}{9}\right)\cdot9 + b$
Simplify Equation: Simplify the equation: $-6 = -7 + b$ .
Solve for Y-Intercept: Add $7$ to both sides to solve for $b$ : $b = 1$ .
Final Equation of Line q: The equation of line q in slope-intercept form is $y = -\frac{7}{9}x + 1$ .

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