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Line $g$ has an equation of $y = 2x + 1$ . Line $h$ includes the point $(-5,2)$ and is perpendicular to line $g$ . What is the equation of line $h$ ? $\newline$ 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. Line

g

has an equation of

y = 2x + 1

. Line

h

includes the point

(-5,2)

and is perpendicular to line

g

. What is the equation of line

h

?

\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 $h$ is perpendicular to line $g$ . $\newline$ Are their slopes the same or opposite reciprocals? $\newline$ Slopes of perpendicular lines are opposite reciprocals.
Equation of Line g: Equation of line g: $\newline$ $y = 2x + 1$ $\newline$ Find the slope of line g. $\newline$ Compare $y = 2x + 1$ with $y = mx + b$ . $\newline$ $m = 2$ $\newline$ Slope of line g: $2$
Slope of Line $h$ : Line $h$ is perpendicular to $g$ . $\newline$ Slope of line $g$ : $2$ $\newline$ Find the slope of line $h$ . $\newline$ Opposite reciprocal of $2$ is $-\frac{1}{2}$ . $\newline$ Slope of line $h$ : $-\frac{1}{2}$
Y-Intercept Calculation: For line $h$ : $\newline$ Slope ( $m$ ): $-\frac{1}{2}$ $\newline$ Point: $(-5, 2)$ $\newline$ Plug these values in $y = mx + b$ and find the y-intercept. $\newline$ $2 = -\frac{1}{2}(-5) + b$ $\newline$ $2 = \frac{5}{2} + b$ $\newline$ $2 - \frac{5}{2} = b$ $\newline$ $\frac{4}{2} - \frac{5}{2} = b$ $\newline$ $-\frac{1}{2} = b$
Equation of Line h: For line h: $\newline$ Slope $m$ : $-\frac{1}{2}$ $\newline$ y-intercept $b$ : $-\frac{1}{2}$ $\newline$ What is the equation of the line h in slope-intercept form? $\newline$ Substitute $-\frac{1}{2}$ for $m$ and $-\frac{1}{2}$ for $b$ in $y = mx + b$ . $\newline$ y = $-\frac{1}{2}x - \frac{1}{2}$

More problems from Write an equation for a parallel or perpendicular line

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\text{(A)horizontal line}

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