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 write the equation of the line in slope-intercept form.

To find the equation of the line in slope-intercept form (\(y = mx + b\)), we need two key components:

1. **Slope** (\(m\)): The slope is calculated using two points on the line.
2. **Intercept** (\(b\)): Once we have the slope, we use one of the points to find the y-intercept.

The two points given are: \((-3, 1)\) and \((2, -4)\).

### Step 1: Find the slope (\(m\))
The formula for the slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the points:
\[
m = \frac{-4 - 1}{2 - (-3)} = \frac{-4 - 1}{2 + 3} = \frac{-5}{5} = -1
\]
So, the slope \(m = -1\).

### Step 2: Use the slope-intercept form to find \(b\)
The slope-intercept form is \(y = mx + b\). We can substitute one of the points, say \((-3, 1)\), into this equation and solve for \(b\).

Substitute \(x = -3\), \(y = 1\), and \(m = -1\):
\[
1 = (-1)(-3) + b
\]
\[
1 = 3 + b
\]
\[
b = 1 - 3 = -2
\]

### Step 3: Write the equation
Now that we have both the slope \(m = -1\) and the intercept \(b = -2\), the equation of the line is:
\[
y = -x - 2
\]

Would you like more details on this or have any questions?

Here are 5 related questions you could explore:
1. How would the equation change if the slope were positive instead of negative?
2. Can you calculate the slope for any two points on a line?
3. What does the y-intercept represent geometrically?
4. How do we determine the x-intercept from this equation?
5. How would the line look if the slope were \(m = 0\)?

**Tip**: Always remember to simplify your slope and double-check that the line passes through both given points after finding the equation!

write the equation of the line in slope-intercept form.

Find the equation of a line passing through the points (-3, 1) and (2, -4) using the slope-intercept form y = mx + b. This problem covers concepts in algebra and linear equations, suitable for students in Grades 8-10.

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