To solve the problem and determine the correct graph, we need to analyze the equation of the linear function provided:

The equation is:
$4x - 12y - 24 = 0$

Step 1: Rewrite in slope-intercept form

Solve for $y$: $4x - 12y = 24$ $-12y = -4x + 24$ $y = \frac{1}{3}x - 2$

So the slope is $\frac{1}{3}$ and the y-intercept is $-2$.

Step 2: Find the x- and y-intercepts

• Y-intercept: Set $x = 0$: $y = \frac{1}{3}(0) - 2 = -2$ So the y-intercept is $(0, -2)$.

• X-intercept: Set $y = 0$: $0 = \frac{1}{3}x - 2$ $\frac{1}{3}x = 2 \quad \Rightarrow \quad x = 6$ So the x-intercept is $(6, 0)$.

Step 3: Match the graph

The correct graph must have the points $(0, -2)$ and $(6, 0)$. Upon inspection of the options:

• The first graph shows $(0, -2)$ and $(-6, 0)$ — incorrect.
• The second graph shows $(0, -2)$ and $(6, 0)$ — correct.
• The third graph does not match either intercept.

Answer:

The correct choice is the second graph with intercepts $(0, -2)$ and $(6, 0)$.

Let me know if you want additional details or have questions! Here are 5 related questions to consider:

1. What does the slope of a line represent geometrically?
2. How can you verify graphically if a point lies on a given line?
3. Why is slope-intercept form useful for graphing?
4. What steps are involved in converting a standard form equation to slope-intercept form?
5. How would you graph this equation without calculating intercepts?

Tip: Always confirm the intercepts and slope visually on the graph for accuracy!