https://file.aiquickdraw.com/mathbot/file/1727412047386co9eubnb.jpg

To solve the problem in the image, we need to find the equation of a line passing through the points \((-6, -7)\) and \((-3, -4)\) in slope-intercept form (\(y = mx + b\)).

### Steps:

1. **Find the slope \(m\)**:
   The slope formula is:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Using the points \((-6, -7)\) and \((-3, -4)\), we get:
   \[
   m = \frac{-4 - (-7)}{-3 - (-6)} = \frac{-4 + 7}{-3 + 6} = \frac{3}{3} = 1
   \]
   So, the slope \(m = 1\).

2. **Use the point-slope form**:
   The point-slope form of a line is:
   \[
   y - y_1 = m(x - x_1)
   \]
   Using the slope \(m = 1\) and the point \((-6, -7)\), we substitute:
   \[
   y - (-7) = 1(x - (-6)) \Rightarrow y + 7 = x + 6
   \]

3. **Convert to slope-intercept form**:
   Simplify the equation:
   \[
   y = x + 6 - 7 \Rightarrow y = x - 1
   \]

### Final Answer:
The equation of the line is:
\[
y = x - 1
\]

Would you like any further clarification or details?

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Here are 5 related questions to consider:
1. What is the general form of the equation of a line, and how is it different from slope-intercept form?
2. How do you find the slope if the coordinates contain fractions?
3. What happens to the slope of the line if the two points have the same x-coordinate?
4. Can you find the equation of a line given one point and the slope?
5. How do you graph a line if only the equation is provided?

**Tip**: Always double-check your slope calculation, as a small mistake there affects the entire equation!

Find the linear equation whose graph passes through the given points (-6, -7) and (-3, -4). Write the equation in slope-intercept form.

Learn how to find the linear equation in slope-intercept form that passes through the points (-6, -7) and (-3, -4). This step-by-step guide explains how to calculate the slope and use it to derive the equation. Suitable for students in Grades 8-10.

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