To find the equation of a line in slope-intercept form ($y = mx + b$), we follow these steps:

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

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute $(x_1, y_1) = (-3, 5)$ and $(x_2, y_2) = (9, 1)$: $m = \frac{1 - 5}{9 - (-3)} = \frac{-4}{9 + 3} = \frac{-4}{12} = \frac{-1}{3}$

Step 2: Use point-slope form to find the equation:

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ Substitute $m = -\frac{1}{3}$ and one of the points, say $(-3, 5)$: $y - 5 = -\frac{1}{3}(x - (-3))$ Simplify: $y - 5 = -\frac{1}{3}(x + 3)$ Distribute the slope: $y - 5 = -\frac{1}{3}x - 1$ Add 5 to both sides: $y = -\frac{1}{3}x + 4$

Final Answer:

The equation of the line in slope-intercept form is: $y = -\frac{1}{3}x + 4$

Would you like further clarification or details? Here are five related questions:

1. What is the slope of a line parallel to this one?
2. How do you find the equation of a line perpendicular to this one?
3. Can we rewrite the equation in standard form ($Ax + By = C$)?
4. How would the graph of this equation look?
5. How do we verify that both points satisfy the final equation?

Tip: Always use the slope formula carefully to avoid sign errors!