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The problem shown in the image asks to find the slope-intercept equation of a line that passes through two points: (5, 0) and (-1, 4). To solve this:

1. **Find the slope (m)** using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting the points (5, 0) and (-1, 4) into the formula:
   \[
   m = \frac{4 - 0}{-1 - 5} = \frac{4}{-6} = -\frac{2}{3}
   \]

2. **Use the slope-intercept form of a line**:
   \[
   y = mx + b
   \]
   We already know \( m = -\frac{2}{3} \), so now use one of the points to find \( b \) (the y-intercept). Let's use the point (5, 0).

   Substitute \( x = 5 \), \( y = 0 \), and \( m = -\frac{2}{3} \) into the equation:
   \[
   0 = -\frac{2}{3}(5) + b
   \]
   \[
   0 = -\frac{10}{3} + b
   \]
   Solving for \( b \):
   \[
   b = \frac{10}{3}
   \]

3. **Write the final equation**:
   \[
   y = -\frac{2}{3}x + \frac{10}{3}
   \]

This is the slope-intercept form of the line passing through (5, 0) and (-1, 4).

Would you like further clarification on any of the steps?

Here are 5 related questions:
1. What is the significance of the slope in a linear equation?
2. How would the equation change if the points were (5, 0) and (0, 4)?
3. How can you convert the slope-intercept form into point-slope form?
4. What happens to the slope if the x-coordinates of the two points are the same?
5. How can you find the equation of a line given a point and the slope?

**Tip:** Always reduce fractions when finding the slope to simplify the equation.

Write a slope-intercept equation for a line that passes through (5,0) and (-1,4).

Learn how to find the slope-intercept equation for a line passing through the points (5,0) and (-1,4). This solution includes the slope formula, step-by-step calculations, and final equation. Suitable for Grades 8-10 students.

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