A line passes through the point (-1,-8) and has a slope of 5. Write an equation in slope-intercept form for this line.

To write the equation of a line in slope-intercept form \( y = mx + b \), we need the slope \( m \) and the y-intercept \( b \).

Given:
- Point \( (-1, -8) \)
- Slope \( m = 5 \)

We can use the point-slope form of a line:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is a point on the line. Substituting the values:

\[
y - (-8) = 5(x - (-1))
\]

Simplify:
\[
y + 8 = 5(x + 1)
\]

Expanding this:
\[
y + 8 = 5x + 5
\]

Subtract 8 from both sides to isolate \( y \):
\[
y = 5x - 3
\]

### Final Answer
The equation of the line in slope-intercept form is:
\[
y = 5x - 3
\]

Would you like further details or have any questions?

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Here are five related questions for practice:
1. How would you find the equation of a line passing through \( (2, 3) \) with a slope of \( -4 \)?
2. If a line has a slope of \( 0 \), what is its equation if it passes through \( (1, -5) \)?
3. How can you determine if two lines are parallel given their equations?
4. How would you convert the equation \( 3x + 4y = 12 \) to slope-intercept form?
5. What is the equation of a line perpendicular to \( y = 2x + 1 \) that passes through \( (3, 4) \)?

**Tip:** When finding the equation of a line with a known slope and point, the point-slope form \( y - y_1 = m(x - x_1) \) is often the most direct method.

Learn how to find the equation of a line that passes through the point (-1, -8) with a slope of 5, written in slope-intercept form. This problem covers key algebraic concepts, including linear equations and slope-intercept form. Ideal for Grades 8-10 students.

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