Let's analyze the equation given in the problem:

The equation provided is: $3x - 4y = 12$

To solve this and find the x- and y-intercepts, we'll set $y = 0$ to find the x-intercept, and $x = 0$ to find the y-intercept.

Step 1: Finding the x-intercept

For the x-intercept, set $y = 0$: $3x - 4(0) = 12 \Rightarrow 3x = 12 \Rightarrow x = 4$ So, the x-intercept is $(4, 0)$.

Step 2: Finding the y-intercept

For the y-intercept, set $x = 0$: $3(0) - 4y = 12 \Rightarrow -4y = 12 \Rightarrow y = -3$ So, the y-intercept is $(0, -3)$.

Step 3: Choosing the Correct Graph

The correct graph should have the intercepts at $(4, 0)$ and $(0, -3)$.

Upon inspecting the options, the graph with these intercepts is the last option.

Therefore, the answer is: The last graph is the correct one, as it has the intercepts $(4, 0)$ and $(0, -3)$.

Would you like more details on this solution, or do you have any questions?

Here are 5 related questions to consider:

1. How do you determine the slope of a line from its equation?
2. What would the graph look like if the equation was $3x + 4y = 12$ instead?
3. How would you find intercepts for equations with more variables, such as $3x - 4y + z = 12$?
4. How can you quickly verify if a point lies on a given line?
5. How can the equation $3x - 4y = 12$ be converted into slope-intercept form?

Tip: When working with linear equations, intercepts are often the quickest way to graph the line accurately.