https://file.aiquickdraw.com/mathbot/file/17272793251756tcb3f7m.jpg

Let's solve the problem given in the image. 

We are asked to find the equation of a line passing through the point \((-2, 9)\) with a slope \(m = -4\), both in **point-slope form** and **slope-intercept form**.

### 1. Point-Slope Form:

The point-slope form of a line is given by the equation:

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

Where:
- \((x_1, y_1)\) is the point on the line (in this case, \((-2, 9)\)),
- \(m\) is the slope (here, \(m = -4\)).

Substitute the given values:

\[
y - 9 = -4(x - (-2)) \implies y - 9 = -4(x + 2)
\]

Thus, the point-slope form is:

\[
y - 9 = -4(x + 2)
\]

### 2. Slope-Intercept Form:

The slope-intercept form is:

\[
y = mx + b
\]

We already know the slope \(m = -4\). Now we use the point \((-2, 9)\) to solve for the intercept \(b\).

Substitute the values into the slope-intercept form equation:

\[
9 = -4(-2) + b
\]

Simplify:

\[
9 = 8 + b \implies b = 1
\]

So the slope-intercept form is:

\[
y = -4x + 1
\]

### Summary:

- **Point-Slope Form:** \( y - 9 = -4(x + 2) \)
- **Slope-Intercept Form:** \( y = -4x + 1 \)

---

Would you like more details or have any further questions?

Here are 5 related questions to consider:
1. How would the point-slope form change if the slope were positive?
2. Can you derive the slope from two given points instead of having it provided?
3. What is the general form of a linear equation, and how do we convert from slope-intercept form to general form?
4. How do parallel lines relate in terms of slope?
5. What are the steps to graph a line using slope-intercept form?

**Tip:** When converting from point-slope form to slope-intercept form, always distribute the slope first and then solve for \(y\).

Given a line that passes through the points (-2, 9) and m = -4 write the equation of this line.

Learn how to write the equations of a line in both point-slope and slope-intercept forms. This guide includes step-by-step solutions to find the equations for a line passing through the point (-2, 9) with a slope of -4, suitable for students in Grades 8-10.

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