https://file.aiquickdraw.com/mathbot/file/17303859609340gep0fh6.jpg

To solve this problem, we need to determine both the slope and the y-intercept of the linear function \( g \) that passes through the points \((-4, 4)\) and \((4, 6)\).

### Step 1: Calculate the Slope
The slope \( m \) of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the given points:
- \((x_1, y_1) = (-4, 4)\)
- \((x_2, y_2) = (4, 6)\)

\[
m = \frac{6 - 4}{4 - (-4)} = \frac{2}{8} = \frac{1}{4}
\]

So, the slope \( m = \frac{1}{4} \).

### Step 2: Calculate the Y-Intercept
To find the y-intercept \( b \), we can use the point-slope form of the line:
\[
y = mx + b
\]
Substituting \( m = \frac{1}{4} \) and using one of the points, say \((-4, 4)\):
\[
4 = \frac{1}{4}(-4) + b
\]
\[
4 = -1 + b
\]
\[
b = 5
\]

### Conclusion
The slope is \( \frac{1}{4} \) and the y-intercept is \( 5 \). 

### Answer
The correct choice is:
- **The slope is \( \frac{1}{4} \) and the y-intercept is \( 5 \)**.

Would you like more details or have any questions?

Here are five related questions to deepen your understanding:
1. How would the graph change if the slope were negative?
2. How can you find the x-intercept of a line given its equation?
3. What is the general equation of a line in slope-intercept form?
4. How does the slope affect the steepness of a line?
5. Can you find the slope of a vertical or horizontal line?

**Tip:** When finding the slope between two points, make sure to consistently use \((x_1, y_1)\) and \((x_2, y_2)\) in the same order to avoid sign errors.

The graph of linear function g passes through the points (-4, 4) and (4, 6), as shown. What are the slope and y-intercept of the graph g?

Solve for the slope and y-intercept of a linear function passing through points (-4, 4) and (4, 6). This solution provides a step-by-step approach to finding the slope and intercept, ideal for students in Grades 7-9.

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