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The equation of line $s$ is $y = \frac{3}{5}x + \frac{2}{5}$ . Line $t$ , which is parallel to line $s$ , includes the point $(2,1)$ . What is the equation of line $t$ ? $\newline$ 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 of line

s

is

y = \frac{3}{5}x + \frac{2}{5}

. Line

t

, which is parallel to line

s

, includes the point

(2,1)

. What is the equation of line

t

?

\newline

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

Check Slope Match: Line $t$ is parallel to line $s$ . Do their slopes match? Yes, parallel lines have the same slope.
Find Slope of Line s: Equation of line s: $\newline$ $y = \frac{3}{5}x + \frac{2}{5}$ $\newline$ Find the slope of line s. $\newline$ Compare $y = \frac{3}{5}x + \frac{2}{5}$ with $y = mx + b$ . $\newline$ $m = \frac{3}{5}$ $\newline$ Slope of line s: $\frac{3}{5}$
Find Slope of Line $t$ : Line $t$ is parallel to $s$ . $\newline$ Slope of line $s$ : $\frac{3}{5}$ $\newline$ Find the slope of line $t$ . $\newline$ Since line $t$ is parallel to line $s$ , its slope is also $\frac{3}{5}$ . $\newline$ Slope of line $t$ : $\frac{3}{5}$
Find y-intercept of Line t: For line t: $\newline$ Slope (m): $\frac{3}{5}$ $\newline$ Point: $(2, 1)$ $\newline$ Plug these values in $y = mx + b$ and find the y-intercept. $\newline$ $1 = \frac{3}{5}(2) + b$ $\newline$ $1 = \frac{6}{5} + b$ $\newline$ Subtract $\frac{6}{5}$ from both sides to solve for $b$ . $\newline$ $1 - \frac{6}{5} = b$ $\newline$ $\frac{5}{5} - \frac{6}{5} = b$ $\newline$ $-\frac{1}{5} = b$
Equation of Line t: For line t: $\newline$ Slope $m$ : $\frac{3}{5}$ $\newline$ y-intercept $b$ : $-\frac{1}{5}$ $\newline$ What is the equation of the line t in slope-intercept form? $\newline$ Substitute $\frac{3}{5}$ for $m$ and $-\frac{1}{5}$ for $b$ in $y = mx + b$ . $\newline$ $y = \frac{3}{5}x - \frac{1}{5}$

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