To determine the equation of the line passing through the points $(-8, 1)$ and $(0, -5)$, we can proceed as follows:

1. Calculate the Slope (m): The slope $m$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting $(x_1, y_1) = (-8, 1)$ and $(x_2, y_2) = (0, -5)$, $m = \frac{-5 - 1}{0 + 8} = \frac{-6}{8} = -\frac{3}{4}$

2. Use the Point-Slope Form to Find the Equation: The point-slope form of a line is: $y - y_1 = m(x - x_1)$ Using the point $(0, -5)$ and the slope $-\frac{3}{4}$, $y + 5 = -\frac{3}{4}x$ Simplifying, we get: $y = -\frac{3}{4}x - 5$

3. Identify the Correct Answer: The equation of the line is: $y = -\frac{3}{4}x - 5$ This matches the third option.

Answer:

The correct answer is:

• $y = -\frac{3}{4}x - 5$

Would you like further details or have any questions?

Here are five related questions for further exploration:

1. How would you find the equation of a line passing through two different points?
2. What would be the equation if the points were $(1, 2)$ and $(3, 4)$?
3. How can you determine if two lines are parallel using their slopes?
4. What does it mean geometrically if the slope of a line is negative?
5. How do you convert from point-slope form to slope-intercept form?

Tip: Always check your calculations when determining the slope to ensure accuracy in finding the line equation.