The problem asks for the equation of a line passing through the points $(-3, 5)$ and $(2, -1)$.

To find the equation of the line, we can use the point-slope form or the slope-intercept form of the equation of a line. We'll start by calculating the slope $m$ using the formula:

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

Where:

• $(x_1, y_1) = (-3, 5)$
• $(x_2, y_2) = (2, -1)$

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

So, the slope $m = -\frac{6}{5}$.

Now, using the point-slope form of the equation of a line:

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

Substituting $m = -\frac{6}{5}$, and using the point $(-3, 5)$:

$y - 5 = -\frac{6}{5}(x + 3)$

Now, simplifying the equation:

$y - 5 = -\frac{6}{5}x - \frac{18}{5}$

Add 5 to both sides (convert 5 to $\frac{25}{5}$):

$y = -\frac{6}{5}x - \frac{18}{5} + \frac{25}{5}$

$y = -\frac{6}{5}x + \frac{7}{5}$

Thus, the equation of the line is:

$y = -\frac{6}{5}x + \frac{7}{5}$

Let me know if you would like more details or explanations!

Here are 5 related questions:

1. How do you calculate the slope between two points in general?
2. What is the point-slope form of the equation of a line?
3. How can you convert point-slope form to slope-intercept form?
4. How can you verify that a point lies on a given line?
5. What is the general formula for the equation of a line in standard form?

Tip: You can always use either of the two given points to find the equation once you have the slope, as the result will be the same!