Find the equation of a line with slope m=-4 and containing the point (-2,-3). Write the equation in slope intercept form 

To find the equation of a line in **slope-intercept form**, which is:

\[
y = mx + b
\]

where:
- \( m \) is the slope, and
- \( b \) is the y-intercept.

You are given:
- Slope \( m = -4 \),
- A point on the line \( (-2, -3) \).

### Steps:

1. Use the point-slope form of the line equation:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) \) is the point \( (-2, -3) \).

2. Substitute the given slope \( m = -4 \) and point \( (x_1, y_1) = (-2, -3) \):
   \[
   y - (-3) = -4(x - (-2))
   \]
   Simplifying:
   \[
   y + 3 = -4(x + 2)
   \]

3. Distribute the slope \( -4 \) on the right-hand side:
   \[
   y + 3 = -4x - 8
   \]

4. Solve for \( y \) by subtracting 3 from both sides:
   \[
   y = -4x - 8 - 3
   \]
   \[
   y = -4x - 11
   \]

### Final Equation:
The equation of the line in slope-intercept form is:
\[
y = -4x - 11
\]

Would you like more details on any step? Here are five related questions to explore further:

1. How can we convert an equation from point-slope form to slope-intercept form?
2. What happens to the graph of a line when the slope is negative?
3. Can you explain how to find the y-intercept from a given point and slope?
4. How do you graph a line using the slope-intercept equation?
5. What is the significance of the slope in the equation of a line?

**Tip:** Always check your final equation by substituting the given point into it to verify it's correct!

Find the equation of a line with slope m=-4 and containing the point (-2,-3). Write the equation in slope intercept form.

Discover how to find the equation of a line with a slope of -4 that passes through the point (-2, -3). This detailed guide walks you through the step-by-step process using slope-intercept and point-slope forms, perfect for students in Grades 8-10.

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