To find the equation of the line through the given points $(-1, 5)$ and $(2, 2)$, we can use the slope-intercept form of a line, which is:

$y = mx + b$

Step 1: Calculate the slope $m$

The slope $m$ is calculated using the formula:

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

Using the points $(-1, 5)$ and $(2, 2)$:

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

Substitute into the formula:

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

Step 2: Use the point-slope form

We can use one of the points, say $(2, 2)$, along with the slope to find the equation.

The point-slope form is:

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

Substitute $m = -1$ and $(x_1, y_1) = (2, 2)$:

$y - 2 = -1(x - 2)$

Simplify:

$y - 2 = -x + 2$

$y = -x + 4$

Thus, the equation of the line in slope-intercept form is:

$\boxed{y = -x + 4}$

Would you like further clarification or have any questions?

Here are 5 related questions to consider:

1. How do you find the slope between any two points?
2. What is the difference between slope-intercept and point-slope forms of a line?
3. How would the equation change if the points were reversed?
4. Can you derive the equation without calculating the slope first?
5. What does the slope of this line tell you about its steepness and direction?

Tip: Always double-check the signs when calculating the slope, especially when dealing with negative coordinates.