Write an equation for the line through the point (-8,-8) and parallel to the line y=4x-9 in point-slope form y=y0+m(x-x0)

To find the equation of the line through the point (-8, -8) and parallel to the line \( y = 4x - 9 \), we need to use the point-slope form of a line, which is:

\[
y - y_0 = m(x - x_0)
\]

where \( (x_0, y_0) \) is a point on the line and \( m \) is the slope.

### Step-by-step:
1. **Find the slope**: The line given is \( y = 4x - 9 \), and its slope is \( m = 4 \). Since parallel lines have the same slope, the slope of the line we need is also \( m = 4 \).
   
2. **Use the point (-8, -8)**: Substituting \( x_0 = -8 \), \( y_0 = -8 \), and \( m = 4 \) into the point-slope form equation:

\[
y - (-8) = 4(x - (-8))
\]

3. **Simplify**: 

\[
y + 8 = 4(x + 8)
\]

This is the equation of the line in point-slope form.

Would you like further details or have any questions?

Here are 5 related questions you might find helpful:
1. How do you find the slope between two points?
2. What is the difference between point-slope form and slope-intercept form?
3. How do you convert point-slope form to slope-intercept form?
4. What does it mean for two lines to be parallel?
5. Can you find the equation of a line perpendicular to a given line?

**Tip**: Always double-check the slope when finding the equation of a line parallel or perpendicular to another line!

Learn how to write the equation of a line passing through the point (-8, -8) and parallel to the line y=4x-9 using point-slope form. This step-by-step solution includes key concepts in algebra and linear equations. Suitable for students in Grades 8-10.

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