https://file.aiquickdraw.com/mathbot/file/17284154316853eby8rrj.jpg

To solve the problem using point-slope form and write the equation of the line in slope-intercept form, we can analyze the information provided in the image.

### Step 1: Identify the Slope and Point
From the graph, we know:
- The slope \( m = -\frac{1}{4} \)
- A point on the line is \( (-6, -3) \)

### Step 2: Use the Point-Slope Form Equation
The point-slope form of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
Where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line.

Substitute the values:
- \( m = -\frac{1}{4} \)
- \( (x_1, y_1) = (-6, -3) \)

\[
y - (-3) = -\frac{1}{4}(x - (-6))
\]
This simplifies to:
\[
y + 3 = -\frac{1}{4}(x + 6)
\]

### Step 3: Solve for \( y \) (Convert to Slope-Intercept Form)
To convert this to slope-intercept form (\( y = mx + b \)), distribute the slope on the right-hand side:
\[
y + 3 = -\frac{1}{4}x - \frac{1}{4} \times 6
\]
\[
y + 3 = -\frac{1}{4}x - \frac{6}{4}
\]
\[
y + 3 = -\frac{1}{4}x - \frac{3}{2}
\]

Now, subtract 3 from both sides to isolate \( y \):
\[
y = -\frac{1}{4}x - \frac{3}{2} - 3
\]
\[
y = -\frac{1}{4}x - \frac{3}{2} - \frac{6}{2}
\]
\[
y = -\frac{1}{4}x - \frac{9}{2}
\]

### Final Equation:
The slope-intercept form of the equation is:
\[
y = -\frac{1}{4}x - \frac{9}{2}
\]

Let me know if you'd like further details or have any questions!

Here are 5 related questions you might find interesting:
1. How do you derive the slope-intercept form from the general form of a line equation?
2. What does the slope of a line tell us about the direction of the line?
3. How can you verify that the point \((-6, -3)\) lies on the line you just found?
4. What would happen to the graph of this line if the slope were positive?
5. How do you find the x- and y-intercepts from the equation of a line?

**Tip**: Always check your point by substituting it back into the final equation to ensure accuracy!

Use the point-slope form to write an equation of the line. Write the equation in slope-intercept form.

Learn how to find the equation of a line using the point-slope form and convert it to slope-intercept form. In this problem, we are given the slope -1/4 and the point (-6, -3). Suitable for students in Grades 8-10.

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