A function f is given.
f(x) = 9x + 8
(a) Sketch a graph of f.

To sketch the graph of the linear function \( f(x) = 9x + 8 \), follow these steps:

### Step 1: Identify the slope and y-intercept
The equation \( f(x) = 9x + 8 \) is in the slope-intercept form \( y = mx + b \), where:
- \( m = 9 \) is the slope of the line.
- \( b = 8 \) is the y-intercept (the point where the line crosses the y-axis).

### Step 2: Plot the y-intercept
The y-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the function:
\[
f(0) = 9(0) + 8 = 8
\]
So, the point \( (0, 8) \) is on the graph. Plot this point on the y-axis.

### Step 3: Use the slope to find another point
The slope \( m = 9 \) means that for every 1 unit increase in \( x \), \( y \) increases by 9 units. Starting from the point \( (0, 8) \), move 1 unit to the right (increasing \( x \) by 1) and 9 units up (increasing \( y \) by 9).

This gives another point:
\[
x = 1, \quad f(1) = 9(1) + 8 = 17
\]
So, the point \( (1, 17) \) is also on the graph. Plot this point.

### Step 4: Draw the line
Now, draw a straight line passing through the points \( (0, 8) \) and \( (1, 17) \). This line is the graph of the function \( f(x) = 9x + 8 \).

Would you like me to generate a visual sketch of the graph for you?

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**Relative questions:**
1. What is the slope-intercept form of a line and how does it help in graphing?
2. How would the graph change if the slope were negative, e.g., \( f(x) = -9x + 8 \)?
3. What would be the graph's behavior if the y-intercept was 0?
4. How do you determine points to plot from a given linear equation?
5. How does the graph shift if the equation changes to \( f(x) = 9x + 5 \)?

**Tip:** Always check the slope to understand how steep the line will be and whether it is increasing or decreasing.

A function f is given. f(x) = 9x + 8 (a) Sketch a graph of f.

Learn how to sketch the graph of the linear function f(x) = 9x + 8, using the slope-intercept form to identify the slope and y-intercept. This solution is suitable for students in Grades 9-10, covering key concepts like graphing and interpreting linear equations.

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