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The equation of line $c$ is $y = \frac{1}{8}x + 10$ . Line $d$ is perpendicular to line $c$ and passes through $(-1,1)$ . What is the equation of line $d$ ? $\newline$ 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 of line

c

is

y = \frac{1}{8}x + 10

. Line

d

is perpendicular to line

c

and passes through

(-1,1)

. What is the equation of line

d

?

\newline

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 $d$ is perpendicular to line $c$ . Are their slopes the same or opposite reciprocals? Slopes of perpendicular lines are opposite reciprocals.
Equation of Line c: Equation of line c: $\newline$ $y = \frac{1}{8}x + 10$ $\newline$ Find the slope of line c. $\newline$ Compare $y = \frac{1}{8}x + 10$ with $y = mx + b$ . $\newline$ $m = \frac{1}{8}$ $\newline$ Slope of line c: $\frac{1}{8}$
Slope of Line $d$ : Line $d$ is perpendicular to $c$ . $\newline$ Slope of line $c$ : $\frac{1}{8}$ $\newline$ Find the slope of line $d$ . $\newline$ Opposite reciprocal of $\frac{1}{8}$ is $-8$ . $\newline$ Slope of line $d$ : $-8$
Y-Intercept Calculation: For line $d$ : $\newline$ Slope ( $m$ ): $-8$ $\newline$ Point: $(-1, 1)$ $\newline$ Plug these values in $y = mx + b$ and find the y-intercept. $\newline$ $1 = -8(-1) + b$ $\newline$ $1 = 8 + b$ $\newline$ $1 - 8 = b$ $\newline$ $-7 = b$
Equation of Line d: For line d: $\newline$ Slope $m$ : $-8$ $\newline$ y-intercept $b$ : $-7$ $\newline$ What is the equation of the line d in slope-intercept form? $\newline$ Substitute $-8$ for $m$ and $-7$ for $b$ in $y = mx + b$ . $\newline$ $y = -8x - 7$

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