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The equation of line
v is
y=x+(1)/(7). Parallel to line
v is line
w, which passes through the point
(-1,-2). What is the equation of the w?

The equation of line $v$ is $y=x+\frac{1}{7}$ . Parallel to line $v$ is line $w$ , which passes through the point $(-1,-2)$ . What is the equation of the w?

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Write an equation for a parallel or perpendicular line

Full solution

Q. The equation of line

v

is

y=x+\frac{1}{7}

. Parallel to line

v

is line

w

, which passes through the point

(-1,-2)

. What is the equation of the w?

Slope Match: Line $w$ is parallel to line $v$ . Do their slopes match? Yes, parallel lines have the same slope.
Equation of Line v: Equation of line v: $\newline$ $y = x + \frac{1}{7}$ $\newline$ Find the slope of line v. $\newline$ Compare $y = x + \frac{1}{7}$ with $y = mx + b$ . $\newline$ $m = 1$ $\newline$ Slope of line v: $1$
Slope of Line $v$ : Line $w$ is parallel to $v$ . $\newline$ Slope of line $v$ : $1$ $\newline$ Find the slope of line $w$ . $\newline$ Since $w$ is parallel to $v$ , the slope of $w$ is also $1$ . $\newline$ Slope of line $w$ : $1$
Slope of Line w: For line w: $\newline$ Slope $m$ : $1$ $\newline$ Point: $(-1, -2)$ $\newline$ Plug these values in $y = mx + b$ and find the y-intercept. $\newline$ $-2 = 1(-1) + b$ $\newline$ $-2 = -1 + b$ $\newline$ $-1 = b$
Y-Intercept of Line w: For line w: $\newline$ Slope $m$ : $1$ $\newline$ y-intercept $b$ : $-1$ $\newline$ What is the equation of the line w in slope-intercept form? $\newline$ Substitute $1$ for $m$ and $-1$ for $b$ in $y = mx + b$ . $\newline$ $y = 1x - 1$

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