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Line $u$ has an equation of $y = -x + 7$ . Line $v$ is perpendicular to line $u$ and passes through $(-8,-1)$ . What is the equation of line $v$ ? 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. Line

u

has an equation of

y = -x + 7

. Line

v

is perpendicular to line

u

and passes through

(-8,-1)

. What is the equation of line

v

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

Perpendicular Lines Slopes: Line $v$ is perpendicular to line $u$ .\ Are their slopes the same or opposite reciprocals?\ Slopes of perpendicular lines are opposite reciprocals.
Equation of Line u: Equation of line u: $\newline$ $y = -x + 7$ $\newline$ Find the slope of line u. $\newline$ Compare $y = -x + 7$ with $y = mx + b$ . $\newline$ $m = -1$ $\newline$ Slope of line u: $-1$
Slope of Line $v$ : Line $v$ is perpendicular to $u$ . $\newline$ Slope of line $u$ : $-1$ $\newline$ Find the slope of line $v$ . $\newline$ Opposite reciprocal of $-1$ is $1$ . $\newline$ Slope of line $v$ : $1$
Finding Y-Intercept: For line $v$ : $\newline$ Slope ( $m$ ): $1$ $\newline$ Point: $(-8, -1)$ $\newline$ Plug these values in $y = mx + b$ and find the y-intercept. $\newline$ $-1 = 1*(-8) + b$ $\newline$ $-1 = -8 + b$ $\newline$ $b = -1 + 8$ $\newline$ $b = 7$
Equation of Line v: For line v: $\newline$ Slope $m$ : $1$ $\newline$ y-intercept $b$ : $7$ $\newline$ What is the equation of the line v in slope-intercept form? $\newline$ Substitute $1$ for $m$ and $7$ for $b$ in $y = mx + b$ . $\newline$ $y = 1x + 7$

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