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

Perpendicular Lines Slopes: Line q is perpendicular to line p. Are their slopes the same or opposite reciprocals? Slopes of perpendicular lines are opposite reciprocals.Equation of Line p: Equation of line p: y = (9/7)x - 9 Find the slope of line p. Compare y = (9/7)x - 9 with y = mx + b. m = 9/7 Slope of line p: 9/7Slope of Line q: Line q is perpendicular to p. Slope of line p: 9/7 Find the slope of line q. Opposite reciprocal of 9/7 is -7/9. Slope of line q: -7/9Finding y-intercept: For line q: Slope (m): -7/9 Point: (9, -6) Plug these values in y = mx + b and find the y-intercept. -6 = (-7/9)(9) + b -6 = -7 + b b = -6 + 7 b = 1Equation of Line q: For line q: Slope (m): -7/9 y-intercept (b): 1 What is the equation of the line q in slope-intercept form? Substitute -7/9 for m and 1 for b in y = mx + b. y = (-7/9)x + 1

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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 $q$ ?

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Algebra 1

Write an equation for a parallel or perpendicular line

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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

Perpendicular Lines Slopes: Line $q$ is perpendicular to line $p$ . Are their slopes the same or opposite reciprocals? $\newline$ Slopes of perpendicular lines are opposite reciprocals.
Equation of Line p: Equation of line p: $y = \frac{9}{7}x - 9$ $\newline$ Find the slope of line p. $\newline$ Compare $y = \frac{9}{7}x - 9$ with $y = mx + b$ . $\newline$ $m = \frac{9}{7}$ $\newline$ Slope of line p: $\frac{9}{7}$
Slope of Line q: Line q is perpendicular to p. $\newline$ Slope of line p: $\frac{9}{7}$ $\newline$ Find the slope of line q. $\newline$ Opposite reciprocal of $\frac{9}{7}$ is $-\frac{7}{9}$ . $\newline$ Slope of line q: $-\frac{7}{9}$
Finding y-intercept: For line $q$ : $\newline$ Slope ( $m$ ): $-\frac{7}{9}$ $\newline$ Point: $(9, -6)$ $\newline$ Plug these values in $y = mx + b$ and find the y-intercept. $\newline$ $-6 = \left(-\frac{7}{9}\right)(9) + b$ $\newline$ $-6 = -7 + b$ $\newline$ $b = -6 + 7$ $\newline$ $b = 1$
Equation of Line q: For line q: $\newline$ Slope $m$ : $-\frac{7}{9}$ $\newline$ y-intercept $b$ : $1$ $\newline$ What is the equation of the line q in slope-intercept form? $\newline$ Substitute $-\frac{7}{9}$ for $m$ and $1$ for $b$ in $y = mx + b$ . $\newline$ $y = \left(-\frac{7}{9}\right)x + 1$