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Line $c$ has an equation of $y = \frac{4}{3}x + 9$ . Line $d$ is parallel to line $c$ and passes through $(-4,-4)$ . What is the equation of line $d$ ? $\newline$ 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

c

has an equation of

y = \frac{4}{3}x + 9

. Line

d

is parallel to line

c

and passes through

(-4,-4)

. What is the equation of line

d

?

\newline

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

Parallel Lines Slopes Match: Line $d$ is parallel to line $c$ . Do their slopes match? Yes, parallel lines have the same slope.
Equation of Line c: Equation of line c: $\newline$ $y = \frac{4}{3}x + 9$ $\newline$ Find the slope of line c. $\newline$ Compare $y = \frac{4}{3}x + 9$ with $y = mx + b$ . $\newline$ $m = \frac{4}{3}$ $\newline$ Slope of line c: $\frac{4}{3}$
Slope of Line d: Line d is parallel to c. $\newline$ Slope of line c: $\frac{4}{3}$ $\newline$ Find the slope of line d. $\newline$ Since line d is parallel to line c, its slope is also $\frac{4}{3}$ . $\newline$ Slope of line d: $\frac{4}{3}$
Finding Y-Intercept: For line $d$ : $\newline$ Slope ( $m$ ): $\frac{4}{3}$ $\newline$ Point: $(-4, -4)$ $\newline$ Plug these values in $y = mx + b$ and find the y-intercept. $\newline$ $-4 = \frac{4}{3}(-4) + b$ $\newline$ $-4 = -\frac{16}{3} + b$ $\newline$ To find $b$ , add $\frac{16}{3}$ to both sides of the equation. $\newline$ $-4 + \frac{16}{3} = b$ $\newline$ $m$ $0$ $\newline$ $m$ $1$
Equation of Line d: For line d: $\newline$ Slope $m$ : $\frac{4}{3}$ $\newline$ y-intercept $b$ : $\frac{4}{3}$ $\newline$ What is the equation of the line d in slope-intercept form? $\newline$ Substitute $\frac{4}{3}$ for $m$ and $\frac{4}{3}$ for $b$ in $y = mx + b$ . $\newline$ $y = \frac{4}{3}x + \frac{4}{3}$

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