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Line $k$ has an equation of $y = \frac{10}{3}x + 9$ . Line $\ell$ includes the point $(-3,-2)$ and is parallel to line $k$ . What is the equation of line $\ell$ ? $\newline$ 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. Line

k

has an equation of

y = \frac{10}{3}x + 9

. Line

\ell

includes the point

(-3,-2)

and is parallel to line

k

. What is the equation of line

\ell

?

\newline

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

Check Parallel Lines: Line is parallel to $k$ . $\newline$ Do their slopes match? $\newline$ Yes, parallel lines have the same slope.
Find Slope of Line $k$ : Equation of line $k$ : $\newline$ $y = \frac{10}{3}x + 9$ $\newline$ Find the slope of line $k$ . $\newline$ Compare $y = \frac{10}{3}x + 9$ with $y = mx + b$ . $\newline$ $m = \frac{10}{3}$ $\newline$ Slope of line $k$ : $\frac{10}{3}$
Find Slope of Line: Line is parallel to $k$ . $\newline$ Slope of line $k$ : $\frac{10}{3}$ $\newline$ Find the slope of line . $\newline$ Since line is parallel to $k$ , its slope will be the same. $\newline$ Slope of line : $\frac{10}{3}$
Find Y-Intercept: For line : $\newline$ Slope $m$ : $\frac{10}{3}$ $\newline$ Point: $(-3, -2)$ $\newline$ Plug these values in $y = mx + b$ and find the y-intercept. $\newline$ $-2 = \frac{10}{3}(-3) + b$ $\newline$ $-2 = -10 + b$ $\newline$ $b = -2 + 10$ $\newline$ $b = 8$
Find Equation of Line: For line : $\newline$ Slope $m$ : $\frac{10}{3}$ $\newline$ y-intercept $b$ : $8$ $\newline$ What is the equation of the line in slope-intercept form? $\newline$ Substitute $\frac{10}{3}$ for $m$ and $8$ for $b$ in $y = mx + b$ . $\newline$ $y = \frac{10}{3}x + 8$

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