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To find the equation of the line passing through the points \((-2, 4)\) and \((1, 1)\), we can use the point-slope formula:

1. **Step 1**: Calculate the slope (\(m\)) using the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Given points:
\[
(x_1, y_1) = (-2, 4) \quad \text{and} \quad (x_2, y_2) = (1, 1)
\]

Substitute the values:
\[
m = \frac{1 - 4}{1 - (-2)} = \frac{-3}{1 + 2} = \frac{-3}{3} = -1
\]

2. **Step 2**: Use the point-slope form of the equation of a line:
\[
y - y_1 = m(x - x_1)
\]
Using one of the points, say \((1, 1)\), and the slope \(m = -1\):
\[
y - 1 = -1(x - 1)
\]

3. **Step 3**: Simplify the equation:
\[
y - 1 = -x + 1
\]
\[
y = -x + 2
\]

So, the equation of the line is:
\[
y = -x + 2
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the general formula for the slope-intercept form of a line?
2. How can you verify that both points satisfy the equation \(y = -x + 2\)?
3. What are the intercepts of the line \(y = -x + 2\)?
4. How would the equation change if the points were different?
5. Can you write the equation of a line parallel to \(y = -x + 2\)?

**Tip**: When calculating the slope, remember that it represents the "rise over run," or how much \(y\) changes compared to \(x\).

Write an equation of the line that passes through the points (-2,4) and (1,1).

Learn how to find the equation of a line passing through the points (-2,4) and (1,1) using the slope formula and point-slope form. This problem is ideal for students in Grades 8-10 covering key concepts like slope and linear equations.

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