https://file.aiquickdraw.com/mathbot/file/1730531643883a0ddcmaz.jpg

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 \((0, -3)\).**

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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.

Find the x- and y-intercepts of the equation 3x - 4y = 12 and select the correct graph that matches the intercepts plotted.

Learn how to find the x- and y-intercepts for the equation 3x - 4y = 12 and choose the correct graph that matches the intercepts plotted. This problem explores linear equations in standard form and the use of intercepts for graphing. Ideal for students in Grades 8-10.

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