https://file.aiquickdraw.com/mathbot/file/1728574389857u9luocvx.jpg

Let's analyze the graph to find the slope and y-intercept of the linear function.

1. **Finding the slope:**
   The slope \(m\) of a line is calculated as:
   \[
   m = \frac{\text{change in } y}{\text{change in } x} = \frac{\Delta y}{\Delta x}
   \]
   Looking at the graph, we can observe two points:
   - One point is at \((-3, -5)\).
   - Another point is at \((3, 4)\).

   To find the slope:
   \[
   m = \frac{4 - (-5)}{3 - (-3)} = \frac{4 + 5}{3 + 3} = \frac{9}{6} = \frac{3}{2}
   \]
   So, the slope is \( \frac{3}{2} \).

2. **Finding the y-intercept:**
   The y-intercept is where the line crosses the y-axis. From the graph, we see that the line crosses the y-axis at \( y = -1 \).

Thus:
- The slope of the linear function is \( \frac{3}{2} \).
- The y-intercept of the linear function is \( -1 \).

Would you like any further details on the calculation process?

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Here are 5 related questions for further exploration:
1. What is the equation of the line in slope-intercept form \(y = mx + b\)?
2. How does changing the slope affect the steepness of a line?
3. What is the x-intercept of this line?
4. How would the graph look if the slope was negative?
5. Can a line have no y-intercept? If so, when?

**Tip:** When calculating the slope between two points, always remember to subtract the coordinates in the same order (i.e., \(\Delta y\) and \(\Delta x\) correspond to the same points).

The graph of a linear function is shown. The slope of the linear function shown is ____. The y-intercept of the linear function is ____.

Learn how to determine the slope and y-intercept of a linear function from a graph. This problem involves using the slope formula and identifying the y-intercept from the graph. Suitable for students in Grades 8-10.

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