Line $v$ has an equation of $y = -\frac{1}{5}x + 9$ . Line $w$ includes the point $(-10,1)$ and is parallel 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 = -\frac{1}{5}x + 9

. Line

w

includes the point

(-10,1)

and is parallel 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.

Find Slope of Line v: Determine the slope of line v. Line v has an equation of $y = -\frac{1}{5}x + 9$ . The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. Therefore, the slope of line v is $-\frac{1}{5}$ .
Determine Parallel Slope: Since line $w$ is parallel to line $v$ , it must have the same slope. Parallel lines have the same slope. Therefore, the slope of line $w$ is also $-\frac{1}{5}$ .
Calculate Y-Intercept of Line w: Use the point $(-10,1)$ and the slope $-\frac{1}{5}$ to find the y-intercept $(b)$ of line w. $\newline$ We can use the point-slope form of the equation of a line, which is $y - y_1 = m(x - x_1)$ , where $(x_1, y_1)$ is a point on the line and $m$ is the slope. Plugging in the point $(-10,1)$ and the slope $-\frac{1}{5}$ , we get: $\newline$ $1 - y_1 = -\frac{1}{5}(x - (-10))$ $\newline$ $1 - y_1 = -\frac{1}{5}(x + 10)$ $\newline$ Now we need to solve for $-\frac{1}{5}$ $0$ , which is the y-intercept.
Solve for Y-Intercept: Solve for the y-intercept $b$ of line $w$ . $1 = -\frac{1}{5}(-10) + b$ $1 = 2 + b$ Subtract $2$ from both sides to isolate $b$ : $1 - 2 = b$ $-1 = b$ The y-intercept of line $w$ is $-1$ .
Write Equation of Line w: Write the equation of line w in slope-intercept form. $\newline$ We have the slope $m = -\frac{1}{5}$ and the y-intercept $b = -1$ . The slope-intercept form is $y = mx + b$ . Substituting the values we have: $\newline$ $y = -\frac{1}{5}x - 1$ $\newline$ This is the equation of line w in slope-intercept form.