To find the equation of the line that passes through points $A(-3, 4)$ and $B(2, -17)$, we can use the point-slope form of the equation of a line:

Step 1: Find the slope ($m$) of the line

The slope formula is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Where $(x_1, y_1) = (-3, 4)$ and $(x_2, y_2) = (2, -17)$.

Substitute the values: $m = \frac{-17 - 4}{2 - (-3)} = \frac{-21}{5}$

So, the slope of the line is $m = -\frac{21}{5}$.

Step 2: Use the point-slope form

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ We can use either point $A(-3, 4)$ or $B(2, -17)$. Let's use point $A(-3, 4)$:

$y - 4 = -\frac{21}{5}(x - (-3))$

Simplify: $y - 4 = -\frac{21}{5}(x + 3)$ $y - 4 = -\frac{21}{5}x - \frac{63}{5}$ Add 4 to both sides: $y = -\frac{21}{5}x - \frac{63}{5} + 4$ Convert 4 to a fraction with denominator 5: $y = -\frac{21}{5}x - \frac{63}{5} + \frac{20}{5}$ $y = -\frac{21}{5}x - \frac{43}{5}$

Final equation:

The equation of the line is: $y = -\frac{21}{5}x - \frac{43}{5}$

Would you like further details or have any questions?

Here are 5 related questions for further exploration:

1. How can we convert this equation to standard form?
2. What is the slope-intercept form, and how does it differ from the point-slope form?
3. How would the equation change if we used point $B(2, -17)$ instead of $A(-3, 4)$?
4. How do we interpret the slope of $-\frac{21}{5}$ in terms of the line's steepness?
5. How do we find the x- and y-intercepts of this line?

Tip: Always check your slope calculation first, as it's crucial for getting the correct equation of the line.