https://file.aiquickdraw.com/mathbot/file/1727188803436zcckau4b.jpg

The graph in the image shows a straight line passing through two main points: \((-6, -3)\) and \((6, 3)\). To find the equation of the line, we can calculate the slope and use the point-slope form of a linear equation.

### Step 1: Find the slope \( m \)
The slope \( m \) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((-6, -3)\) and \((6, 3)\):

\[
m = \frac{3 - (-3)}{6 - (-6)} = \frac{3 + 3}{6 + 6} = \frac{6}{12} = \frac{1}{2}
\]

### Step 2: Use the point-slope form
Now that we have the slope \( m = \frac{1}{2} \), we can use one of the points, say \((6, 3)\), to find the equation. The point-slope form is:

\[
y - y_1 = m(x - x_1)
\]

Substituting \( m = \frac{1}{2} \), \( x_1 = 6 \), and \( y_1 = 3 \):

\[
y - 3 = \frac{1}{2}(x - 6)
\]

Simplifying:

\[
y - 3 = \frac{1}{2}x - 3
\]

\[
y = \frac{1}{2}x
\]

Thus, the equation of the line is \( y = \frac{1}{2}x \).

### Step 3: Compare with the given options
The correct linear equation should match this form. The options provided are:

- A. \( h(x) = \frac{3}{4}x - 3 \)
- B. \( h(x) = \frac{4}{3}x - 3x \)
- C. \( h(x) = \frac{3}{4}x - 3 \)
- D. \( h(x) = \frac{4}{3}x - 3 \)

None of the given options seem to match the slope \( \frac{1}{2} \). Therefore, the answer doesn't match any of the options directly, indicating there may be a mistake in the options provided or we need to recheck assumptions. 

Would you like to reanalyze this further? Also, here are some related questions:

1. What is the point-slope form of a line, and how is it derived?
2. How does the slope of a line relate to its steepness and direction?
3. Can we identify the y-intercept directly from the graph?
4. How would the equation change if the slope were negative?
5. How would you graph a line given its equation?

**Tip:** When analyzing a graph, always check for the exact coordinates of key points to ensure accuracy.

Which of these could be the linear function whose graph is shown?

Analyze a graph to determine the correct linear function. This problem focuses on understanding linear functions, slope, and interpreting graphs. It is suitable for students in Grades 8-10.

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