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The equation for line $u$ can be written as $y = -2x + 10$ . Line $v$ , which is parallel to line $u$ , includes the point $(-1, 2)$ . What is the equation of line $v$ ?

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Write an equation for a parallel or perpendicular line

Full solution

Q. The equation for line

u

can be written as

y = -2x + 10

. Line

v

, which is parallel to line

u

, includes the point

(-1, 2)

. What is the equation of line

v

?

Slope Match: Line $v$ is parallel to line $u$ . Do their slopes match? Yes, parallel lines have the same slope.
Equation of Line u: Equation of line u: $\newline$ $y = -2x + 10$ $\newline$ Find the slope of line u. $\newline$ Compare $y = -2x + 10$ with $y = mx + b$ . $\newline$ $m = -2$ $\newline$ Slope of line u: $-2$
Slope of Line $v$ : Line $v$ is parallel to $u$ . $\newline$ Slope of line $u$ : $-2$ $\newline$ Find the slope of line $v$ . $\newline$ Since line $v$ is parallel to line $u$ , its slope is also $-2$ . $\newline$ Slope of line $v$ : $-2$
Y-Intercept of Line v: For line v: $\newline$ Slope $m$ : $-2$ $\newline$ Point: $(-1, 2)$ $\newline$ Plug these values in $y = mx + b$ to find the y-intercept $b$ of line v. $\newline$ $2 = -2(-1) + b$ $\newline$ $2 = 2 + b$ $\newline$ $2 - 2 = b$ $\newline$ $0 = b$
Equation of Line v: For line v: $\newline$ Slope $m$ : $-2$ $\newline$ y-intercept $b$ : $0$ $\newline$ What is the equation of the line v in slope-intercept form? $\newline$ Substitute $-2$ for $m$ and $0$ for $b$ in $y = mx + b$ . $\newline$ $y = -2x + 0$ $\newline$ Simplify the equation. $\newline$ $-2$ $0$

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