To determine the equation of the line passing through the points $(8, -7)$ and $(-2, 8)$, follow these steps:

Step 1: Find the slope ($m$) using the formula

$m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the given points: $m = \frac{8 - (-7)}{-2 - 8} = \frac{8 + 7}{-10} = \frac{15}{-10} = -\frac{3}{2}$

Step 2: Use the point-slope form

The equation of a line is: $y - y_1 = m(x - x_1)$ Pick one point, say $(8, -7)$, and substitute: $y - (-7) = -\frac{3}{2}(x - 8)$ Simplify: $y + 7 = -\frac{3}{2}x + 12$ $y = -\frac{3}{2}x + 12 - 7$ $y = -\frac{3}{2}x + 5$

Step 3: Verify the equation

The line passes through $(8, -7)$ and $(-2, 8)$. Testing confirms this equation works.

Thus, the correct equation is: $y = -\frac{3}{2}x + 5$

Correct Option:

$\boxed{y = -3/2x + 5}$

Would you like further clarification or details? Here are 5 questions to expand on this:

1. How do you verify a point lies on a given line equation?
2. What are other forms of a linear equation, and how do they relate?
3. Why is the slope constant between any two points on a line?
4. Can we derive the line equation using both points simultaneously?
5. How does the slope-intercept form help interpret a line's graph?

Tip: Always check your final equation by substituting the given points to confirm accuracy!