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The question from your image states:

**Given:**  
- \( f(x) \) is a linear function.
- \( f(-3) = 4 \)
- \( f(0) = 3 \)

**Find:** An equation for \( f(x) \).

### Solution:

Since \( f(x) \) is a linear function, it can be written in the form:

\[
f(x) = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept.

#### Step 1: Use Given Points to Set Up Equations

We have two points:  
1. \( (-3, 4) \) from \( f(-3) = 4 \)  
2. \( (0, 3) \) from \( f(0) = 3 \)  

Substitute these points into the linear equation:

1. For \( f(-3) = 4 \):  
\[
4 = m(-3) + b
\]

2. For \( f(0) = 3 \):  
\[
3 = m(0) + b \implies b = 3
\]

#### Step 2: Solve for Slope \( m \)

Substitute \( b = 3 \) into the first equation:

\[
4 = m(-3) + 3
\]

Simplify to find \( m \):

\[
4 - 3 = -3m \implies 1 = -3m \implies m = -\frac{1}{3}
\]

#### Step 3: Write the Equation

Now substitute \( m = -\frac{1}{3} \) and \( b = 3 \) back into the linear equation form:

\[
f(x) = -\frac{1}{3}x + 3
\]

### Final Answer:

The equation for \( f(x) \) is:

\[
\boxed{f(x) = -\frac{1}{3}x + 3}
\]

Would you like more details or have any other questions?

### Follow-up Questions:

1. How do you find the slope of a linear function given two points?
2. What is the significance of the y-intercept in a linear equation?
3. How do you graph a linear function on the coordinate plane?
4. How can you determine if a function is linear or non-linear?
5. How does the slope affect the steepness and direction of a line?

#### Tip:
For linear functions, knowing two points is sufficient to determine the equation of the line.

f(x) is a linear function. f(-3) = 4 and f(0) = 3. Find an equation for f(x).

Learn how to find the equation of a linear function given two points: f(-3) = 4 and f(0) = 3. This problem explores key algebraic concepts such as linear functions, slope, and the slope-intercept form, and is suitable for students in Grades 8-10.

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