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 $w$ ? $\newline$ 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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Algebra 1

Write an equation for a parallel or perpendicular line

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Q. 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

\newline

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

Determine slope of line v: Determine the slope of line v. $\newline$ The equation of line v is given as $y = -5x + 6$ . The slope ( $m$ ) of a line in the slope-intercept form $y = mx + b$ is the coefficient of $x$ . Therefore, the slope of line v is $-5$ .
Find slope of line $w$ : Find the slope of line $w$ . Since line $w$ is perpendicular to line $v$ , its slope will be the negative reciprocal of the slope of line $v$ . The negative reciprocal of $-5$ is $\frac{1}{5}$ . Therefore, the slope of line $w$ is $\frac{1}{5}$ .
Use point-slope form: Use the point-slope form to find the equation of line $w$ . We have the slope of line $w$ ( $\frac{1}{5}$ ) and a point that lies on it ( $-1,-2$ ). The point-slope form of a line's equation is $y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is the point on the line. Plugging in the values, we get $y - (-2) = \frac{1}{5}(x - (-1))$ .
Simplify equation to slope-intercept form: Simplify the equation from the point-slope form to the slope-intercept form. $\newline$ Starting with $y + 2 = \frac{1}{5}(x + 1)$ , we distribute the slope on the right side to get $y + 2 = \frac{1}{5}x + \frac{1}{5}$ . Then, we subtract $2$ from both sides to isolate $y$ , resulting in $y = \frac{1}{5}x + \frac{1}{5} - 2$ .
Combine like terms: Combine like terms to get the final equation of line $w$ . We need to combine $\frac{1}{5} - 2$ . Since $2$ is the same as $\frac{10}{5}$ , we have $y = \frac{1}{5}x + \frac{1}{5} - \frac{10}{5}$ , which simplifies to $y = \frac{1}{5}x - \frac{9}{5}$ . This is the equation of line $w$ in slope-intercept form.