Question

line c has an equation of $y = \frac{1}{5}x - 3$. line d, which is parallel to line c, includes the point $(-1, 1)$. what is the equation of line d?
write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Find slope of line d

Parallel lines have equal slopes. Line c has slope $\frac{1}{5}$, so line d's slope $m = \frac{1}{5}$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m = \frac{1}{5}$, $x_1 = -1$, $y_1 = 1$:
$y - 1 = \frac{1}{5}(x - (-1))$
$y - 1 = \frac{1}{5}(x + 1)$

Step3: Convert to slope-intercept form

Expand and solve for y:
$y - 1 = \frac{1}{5}x + \frac{1}{5}$
$y = \frac{1}{5}x + \frac{1}{5} + 1$
$y = \frac{1}{5}x + \frac{6}{5}$

Answer:

$y = \frac{1}{5}x + \frac{6}{5}$