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We are given the following details:

- Line \( v \) has the equation: \( y = -\frac{1}{5}x + 9 \).
- Line \( w \) is parallel to line \( v \) and passes through the point \( (-10, 1) \).

### Step 1: Identify the slope of line \( w \)
Since line \( w \) is parallel to line \( v \), both lines share the same slope. The slope of line \( v \) is \( -\frac{1}{5} \), so the slope of line \( w \) is also \( -\frac{1}{5} \).

### Step 2: Use the point-slope form of the equation of a line
The point-slope form is:

\[
y - y_1 = m(x - x_1)
\]

Where:
- \( m = -\frac{1}{5} \) (the slope),
- \( (x_1, y_1) = (-10, 1) \) (the point through which line \( w \) passes).

Substituting these values into the point-slope form:

\[
y - 1 = -\frac{1}{5}(x - (-10))
\]

Simplifying:

\[
y - 1 = -\frac{1}{5}(x + 10)
\]
\[
y - 1 = -\frac{1}{5}x - 2
\]
\[
y = -\frac{1}{5}x - 2 + 1
\]
\[
y = -\frac{1}{5}x - 1
\]

### Final Answer:
The equation of line \( w \) in slope-intercept form is:

\[
y = -\frac{1}{5}x - 1
\]

Would you like further details or have any questions?

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Here are 5 related questions for further exploration:

1. How do we derive the equation of a line perpendicular to line \( v \) instead of parallel?
2. What changes if line \( w \) passes through a different point, say \( (5, -3) \)?
3. How would we find the point where lines \( v \) and \( w \) intersect if they weren’t parallel?
4. How can we graph both lines on a coordinate plane?
5. How does the slope-intercept form compare to other forms of a line, such as the standard form?

**Tip:** When two lines are parallel, they always have the same slope but different intercepts.

Line v has an equation of y = -1/5x + 9. Line w includes the point (-10, 1) and is parallel to line v. What is the equation of line w?

Learn how to find the equation of a line that is parallel to y = -1/5x + 9 and passes through the point (-10, 1). This problem explores key concepts such as linear equations and the slope of parallel lines, suitable for students in Grades 8-10.

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