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$Line v has an equation of y=-5x+6. Line w includes the point (-1,-2) and is perpendicular to line v. What is the equation of line w ? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers. Submit Work it out Not feeling ready yet? These can help: Slopes of parallel and perpendicular lines Slope-intercept form: write an equation Search$

Line $v$ has an equation of $y=-5 x+6$ . Line $w$ includes the point $(-1,-2)$ and is perpendicular to line $v$ . What is the equation of line $w$ ? $\newline$ Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers. $\newline$ Submit $\newline$ Work it out $\newline$ Not feeling ready yet? These can help: $\newline$ Slopes of parallel and perpendicular lines $\newline$ Slope-intercept form: write an equation $\newline$ Search

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Math Problems

Algebra 1

Write an equation for a parallel or perpendicular line

Full solution

Q. Line

v

has an equation of

y=-5 x+6

. Line

w

includes the point

(-1,-2)

and is perpendicular to line

v

. What is the equation of line

w

\newline

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

\newline

Submit

\newline

Work it out

\newline

Not feeling ready yet? These can help:

\newline

Slopes of parallel and perpendicular lines

\newline

Slope-intercept form: write an equation

\newline

Find Slope of Line $v$ : Line $v$ 's slope is $-5$ . Since $w$ is perpendicular to $v$ , its slope is the opposite reciprocal of $-5$ , which is $\frac{1}{5}$ .
Calculate Y-Intercept of Line w: Using the point $(-1,-2)$ and the slope $\frac{1}{5}$ , plug into $y = mx + b$ to find $b$ , the y-intercept of line $w$ . $\newline$ $-2 = \left(\frac{1}{5}\right)(-1) + b$
Simplify Equation: Simplify the equation: $-2 = -\frac{1}{5} + b$ .
Add $\frac{1}{5}$ to Both Sides: Add $\frac{1}{5}$ to both sides to solve for $b$ : $-2 + \frac{1}{5} = b$ .
Combine Fractions: Convert $-2$ to a fraction with a denominator of $5$ : $-\frac{10}{5} + \frac{1}{5} = b$ .
Write Equation of Line $w$ : Combine the fractions: $-\frac{9}{5} = b$ .
Write Equation of Line w: Combine the fractions: $-\frac{9}{5} = b$ . The slope of line w is $\frac{1}{5}$ and the y-intercept is $-\frac{9}{5}$ . The equation of line w in slope-intercept form is $y = \frac{1}{5}x - \frac{9}{5}$ .