To find the equation of a line passing through two points, we can use the point-slope form of the line equation, which is:

$y - y_1 = m(x - x_1)$

Where:

• $(x_1, y_1)$ is one of the points on the line.
• $m$ is the slope of the line, calculated by:

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

Given the points $(-5, -6)$ and $(1, 3)$:

1. Calculate the slope $m$:

$m = \frac{3 - (-6)}{1 - (-5)} = \frac{3 + 6}{1 + 5} = \frac{9}{6} = \frac{3}{2}$

2. Now, use the point-slope form with the slope $m = \frac{3}{2}$ and one of the points, say $(1, 3)$:

$y - 3 = \frac{3}{2}(x - 1)$

3. To express this in slope-intercept form $y = mx + b$:

Expand and simplify:

$y - 3 = \frac{3}{2}x - \frac{3}{2}$

$y = \frac{3}{2}x - \frac{3}{2} + 3$

$y = \frac{3}{2}x + \frac{3}{2}$

So, the equation of the line is:

$y = \frac{3}{2}x + \frac{3}{2}$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you find the slope of a line if given two points?
2. What is the point-slope form of a line?
3. How can you convert the point-slope form to slope-intercept form?
4. What is the significance of the y-intercept in the slope-intercept form?
5. Can you find the equation of a line parallel to the given line that passes through a different point?

Tip: Always check your slope calculation first, as it determines the accuracy of the line equation.