To find the equation of the line passing through the points $(-3, 6)$ and $(1, 2)$, we use the slope-intercept form of a line equation:

$y = mx + b$

Step 1: Calculate the slope ($m$)

The slope ($m$) is calculated using the formula:

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

Substitute the points $(-3, 6)$ and $(1, 2)$:

$m = \frac{2 - 6}{1 - (-3)} = \frac{-4}{1 + 3} = \frac{-4}{4} = -1$

Step 2: Use the slope and a point to find the y-intercept ($b$)

Substitute the slope $m = -1$ and one of the points (e.g., $(-3, 6)$) into the slope-intercept form $y = mx + b$:

$6 = -1(-3) + b$

$6 = 3 + b$

$b = 6 - 3 = 3$

Step 3: Write the equation of the line

Now that we have $m = -1$ and $b = 3$, the equation of the line is:

$y = -x + 3$

Final Answer:

The equation of the line is:

$y = -x + 3$

Would you like more details or further clarification? Here are 5 related questions you might find interesting:

1. How can you convert this equation to standard form?
2. What is the perpendicular slope to this line?
3. How do you graph the line given the equation $y = -x + 3$?
4. What is the equation of a line parallel to $y = -x + 3$ passing through a different point?
5. How can you find the distance between this line and a point not on the line?

Tip: Always verify your slope and intercept calculations by substituting the points back into the final equation!