We are given two points: \((-1, -4)\) and \((3, 4)\). We need to find the equation of the line in slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

### Step 1: Find the Slope \(m\)
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the given points:
\[
m = \frac{4 - (-4)}{3 - (-1)} = \frac{4 + 4}{3 + 1} = \frac{8}{4} = 2
\]

So, the slope \(m\) is \(2\).

### Step 2: Find the y-intercept \(b\)
Now that we know \(m = 2\), substitute the slope and one of the points (say \((-1, -4)\)) into the slope-intercept form \(y = mx + b\) to find \(b\).

Substituting \((-1, -4)\) into \(y = 2x + b\):
\[
-4 = 2(-1) + b
\]
\[
-4 = -2 + b
\]
\[
b = -4 + 2 = -2
\]

So, the y-intercept \(b\) is \(-2\).

### Final Equation
The equation of the line in slope-intercept form is:
\[
y = 2x - 2
\]

Would you like more details or have any questions about the solution?

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Here are 5 related questions to deepen understanding:
1. What is the meaning of the slope in the context of a line?
2. How do you interpret the y-intercept on a graph?
3. Can you find the x-intercept of this line?
4. How would the equation change if the slope were negative?
5. What happens to the line if you change the y-intercept?

**Tip:** Always double-check your calculations, especially when finding the slope, as small errors can lead to incorrect results.

Learn how to find the equation of a line passing through the points (-1, -4) and (3, 4) using the slope-intercept form. This problem involves calculating the slope, y-intercept, and constructing the equation. Suitable for Grades 7-9.

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