To find the equation of the line in slope-intercept form (\(y = mx + b\)) given the slope \(m = -\frac{4}{5}\) and the point \((10, -7)\), follow these steps:

1. **Substitute** the slope \(m = -\frac{4}{5}\) into the slope-intercept form equation:
   \[
   y = -\frac{4}{5}x + b
   \]

2. **Substitute** the point \((10, -7)\) into the equation where \(x = 10\) and \(y = -7\):
   \[
   -7 = -\frac{4}{5}(10) + b
   \]

3. **Solve for \(b\)**:
   \[
   -7 = -\frac{40}{5} + b
   \]
   \[
   -7 = -8 + b
   \]
   \[
   b = 1
   \]

4. **Write the final equation**:
   \[
   y = -\frac{4}{5}x + 1
   \]

The equation of the line in slope-intercept form is \(y = -\frac{4}{5}x + 1\).

Would you like more details or have any questions? 

Here are 5 related questions you might find interesting:
1. How do you find the equation of a line given two points?
2. What is the point-slope form of a linear equation?
3. How do you convert from point-slope form to slope-intercept form?
4. What is the significance of the slope in a linear equation?
5. How does the y-intercept affect the graph of a line?

**Tip:** Always double-check your calculations by substituting the point back into the final equation to ensure it satisfies the equation.

Discover how to find the equation of a line in slope-intercept form with slope -4/5 that passes through the point (10, -7). This problem covers key algebraic concepts such as slope-intercept form, substitution, and solving for the y-intercept. Suitable for students in Grades 8-10.

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