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.