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.