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The task asks to write a slope-intercept equation for a line that passes through the points (-7, 0) and (4, -2).

### Steps to solve:
1. **Find the slope** (\(m\)) of the line using the slope formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Here, \((x_1, y_1) = (-7, 0)\) and \((x_2, y_2) = (4, -2)\).

   Substituting the values:
   \[
   m = \frac{-2 - 0}{4 - (-7)} = \frac{-2}{4 + 7} = \frac{-2}{11}
   \]
   So, the slope is \(m = -\frac{2}{11}\).

2. **Use the point-slope form of the equation** to find the equation of the line:
   \[
   y - y_1 = m(x - x_1)
   \]
   Using the point \((-7, 0)\) and the slope \(m = -\frac{2}{11}\):
   \[
   y - 0 = -\frac{2}{11}(x - (-7)) = -\frac{2}{11}(x + 7)
   \]

3. **Simplify to slope-intercept form** (\(y = mx + b\)):
   \[
   y = -\frac{2}{11}(x + 7)
   \]
   Distribute the \(-\frac{2}{11}\):
   \[
   y = -\frac{2}{11}x - \frac{14}{11}
   \]

Thus, the slope-intercept form of the equation is:
\[
y = -\frac{2}{11}x - \frac{14}{11}
\]

Would you like a detailed explanation of any of the steps? Let me know!

Here are 5 questions that expand on the topic:

1. How do you find the y-intercept from two points?
2. Can you derive the slope-intercept form directly from the two points without using point-slope form?
3. What does the slope of a line tell you about its direction and steepness?
4. How would the equation change if the line passed through different points?
5. Can a line have an undefined slope? If so, what does that line look like?

**Tip**: When solving for the slope, be careful with signs and subtraction, as they can easily affect your final result.

Write a slope-intercept equation for a line passing through the points (-7, 0) and (4, -2).

Learn how to find the slope-intercept equation of a line that passes through the points (-7, 0) and (4, -2). This problem covers the key concepts of algebra, including slope calculation and converting to slope-intercept form. Suitable for students in Grades 8-10.

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