To write the equation of a line in slope-intercept form $y = mx + b$, the first step is to find the slope $m$ using the given points $(-3, 5)$ and $(6, 2)$.

Step 1: Calculate the slope ($m$) using the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the coordinates: $m = \frac{2 - 5}{6 - (-3)} = \frac{-3}{6 + 3} = \frac{-3}{9} = -\frac{1}{3}$

The slope of the line is $m = -\frac{1}{3}$.

Would you like me to proceed to the next step to find the $y$-intercept ($b$) or clarify this step?

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5 Related Questions:

1. How do you find the $y$-intercept of a line if the slope is known?
2. What is the slope of a horizontal line or vertical line?
3. Can a line passing through two points ever have a slope of $0$?
4. How do you check if two points lie on the same line?
5. What is the importance of slope-intercept form in graphing equations?

Tip: Always simplify the slope to its lowest terms to avoid errors in subsequent calculations.