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The equation for line $j$ can be written as $y = \frac{1}{8}x + 7$ . Parallel to line $j$ is line $k$ , which passes through the point $(-3,-1)$ . What is the equation of line $k$ ? $\newline$ 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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Write an equation for a parallel or perpendicular line

Full solution

Q. The equation for line

j

can be written as

y = \frac{1}{8}x + 7

. Parallel to line

j

is line

k

, which passes through the point

(-3,-1)

. What is the equation of line

k

?

\newline

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

Slope Match: Line $k$ is parallel to line $j$ . Do their slopes match? Yes, parallel lines have the same slope.
Equation of Line j: Equation of line j: $\newline$ $y = \frac{1}{8}x + 7$ $\newline$ Find the slope of line j. $\newline$ Compare $y = \frac{1}{8}x + 7$ with $y = mx + b$ . $\newline$ $m = \frac{1}{8}$ $\newline$ Slope of line j: $\frac{1}{8}$
Slope of Line $k$ : Line $k$ is parallel to $j$ . $\newline$ Slope of line $j$ : $\frac{1}{8}$ $\newline$ Find the slope of line $k$ . $\newline$ Since line $k$ is parallel to line $j$ , its slope is also $\frac{1}{8}$ . $\newline$ Slope of line $k$ : $\frac{1}{8}$
Y-Intercept of Line k: For line k: $\newline$ Slope $m$ : $\frac{1}{8}$ $\newline$ Point: $(-3, -1)$ $\newline$ Plug these values in $y = mx + b$ and find the y-intercept. $\newline$ $-1 = \frac{1}{8}(-3) + b$ $\newline$ $-1 = -\frac{3}{8} + b$ $\newline$ Add $\frac{3}{8}$ to both sides to solve for b. $\newline$ $-1 + \frac{3}{8} = b$ $\newline$ $-\frac{8}{8} + \frac{3}{8} = b$ $\newline$ $-\frac{5}{8} = b$
Equation of Line k: For line k: $\newline$ Slope $m$ : $\frac{1}{8}$ $\newline$ y-intercept $b$ : $\frac{-5}{8}$ $\newline$ What is the equation of the line k in slope-intercept form? $\newline$ Substitute $\frac{1}{8}$ for $m$ and $\frac{-5}{8}$ for $b$ in $y = mx + b$ . $\newline$ $y = \frac{1}{8}x - \frac{5}{8}$

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