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?

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!