To find the equation of the line passing through the points (-4, -3) and (8, 6), we follow these steps:

1. Find the slope of the line using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$ Where:

• $(x_1, y_1) = (-4, -3)$
• $(x_2, y_2) = (8, 6)$

Substitute the values: $m = \frac{6 - (-3)}{8 - (-4)} = \frac{6 + 3}{8 + 4} = \frac{9}{12} = \frac{3}{4}$

So, the slope $m = \frac{3}{4}$.

2. Use the point-slope form of the equation of a line:

$y - y_1 = m(x - x_1)$ Using the point (-4, -3) and the slope $\frac{3}{4}$: $y - (-3) = \frac{3}{4}(x - (-4))$ Simplify: $y + 3 = \frac{3}{4}(x + 4)$

3. Distribute and solve for $y$:

$y + 3 = \frac{3}{4}x + \frac{3}{4} \times 4$ $y + 3 = \frac{3}{4}x + 3$ Subtract 3 from both sides: $y = \frac{3}{4}x$

Final equation:

$y = \frac{3}{4}x$

This is the equation of the line passing through the points (-4, -3) and (8, 6).

Would you like further details on any part of this solution?

Here are 5 related questions you can explore:

1. How would the equation change if the points were (0, 0) and (8, 6)?
2. What is the significance of the slope in this context?
3. How do you find the slope-intercept form from point-slope form?
4. Can a line have a slope of zero? What would its equation look like?
5. How can you find the distance between the two points used here?

Tip: The slope tells you how steep a line is; it's the ratio of the vertical change to the horizontal change.