Question

line v has an equation of $y = -\frac{1}{5}x + 9$. line w includes the point $(-10, 1)$ and is parallel to line v. what is the equation of line w?
write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Determine slope of line w

Parallel lines have equal slopes. Line \( v \) has equation \( y = -\frac{1}{5}x + 9 \), so slope \( m = -\frac{1}{5} \) for line \( w \).

Step2: Use point - slope form

Point - slope form is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(-10,1) \) and \( m = -\frac{1}{5} \).
Substitute values: \( y - 1 = -\frac{1}{5}(x - (-10)) \)
Simplify the right - hand side: \( y - 1 = -\frac{1}{5}(x + 10) \)

Step3: Convert to slope - intercept form

Distribute \( -\frac{1}{5} \): \( y - 1 = -\frac{1}{5}x-2 \)
Add 1 to both sides: \( y=-\frac{1}{5}x - 2 + 1 \)
Simplify: \( y = -\frac{1}{5}x-1 \)

Answer:

\( y = -\frac{1}{5}x - 1 \)