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The problem asks to transform a linear function based on the changes described.

The graph currently shows a line with a negative slope, and the instructions state:

- The slope will be multiplied by \(-9\).
- The \(y\)-intercept will be increased by 2 units.

### Step 1: Analyze the original function
Looking at the graph:
- The line seems to have a negative slope. Let's assume the equation of the line is of the form \( y = mx + b \), where \(m\) is the slope and \(b\) is the y-intercept.
- From the graph, we see the line intersects the y-axis at \( y = 1 \), so the initial \(y\)-intercept is \( b = 1 \).

### Step 2: Apply the changes
1. **Multiplying the slope by -9**: This means the slope \(m\) of the new line will be \(-9\) times the slope of the original line.
2. **Increasing the y-intercept by 2 units**: The new \(y\)-intercept will be \(1 + 2 = 3\).

### Step 3: The new equation
Thus, the new linear equation will be:
\[
y = -9m x + 3
\]

Where \(m\) is the slope of the original line. Since the problem mentions specific transformations, you need to choose the graph that reflects these changes, showing a steep slope and an increased y-intercept at \(y = 3\).

Would you like a further breakdown of how to apply these transformations on the graph?

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Here are five related questions to extend this concept:

1. How do you determine the slope from a graph?
2. What effect does multiplying the slope have on the steepness of the line?
3. How does increasing the y-intercept shift the graph vertically?
4. Can you graph a linear equation given its slope and y-intercept?
5. How would changing the slope to a positive value affect the graph?

**Tip**: Remember that multiplying the slope by a large number, like -9, makes the line much steeper!

In the function above, the slope will be multiplied by -9, and the y-value of the y-intercept will be increased by 2 units. Which of the following graphs best represents the new function?

Learn how to transform a linear function by multiplying the slope by -9 and shifting the y-intercept up by 2 units. This problem covers linear functions, the slope-intercept form, and graphing transformations. Suitable for students in Grades 8-10.

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