Graph the linear equation.

3x−4y=123x−4y=12

Plot two points on the line to graph the line.

To graph the linear equation \( 3x - 4y = 12 \), we first need to express it in the slope-intercept form \( y = mx + b \). Then, we can find two points that satisfy the equation and plot them on the graph.

### Step 1: Rewrite the Equation in Slope-Intercept Form

Starting with the given equation:

\[
3x - 4y = 12
\]

We can solve for \( y \) by isolating it on one side:

\[
-4y = -3x + 12
\]

Now, divide both sides by \(-4\) to solve for \( y \):

\[
y = \frac{3}{4}x - 3
\]

So, the slope-intercept form is:

\[
y = \frac{3}{4}x - 3
\]

### Step 2: Find Two Points

We can choose any two values for \( x \) to find the corresponding \( y \) values.

1. **Point 1: When \( x = 0 \):**

\[
y = \frac{3}{4}(0) - 3 = -3
\]

So, one point is \( (0, -3) \).

2. **Point 2: When \( x = 4 \):**

\[
y = \frac{3}{4}(4) - 3 = 3 - 3 = 0
\]

So, another point is \( (4, 0) \).

### Step 3: Plot the Points and Draw the Line

Now, you can plot the points \( (0, -3) \) and \( (4, 0) \) on the graph, and then draw a line through them to represent the equation \( 3x - 4y = 12 \).

Here is how the graph would look:

1. **Point (0, -3):** This is the y-intercept, where the line crosses the y-axis.
2. **Point (4, 0):** This is the x-intercept, where the line crosses the x-axis.

Would you like me to plot the graph for you?

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Here are some related questions:
1. How do you find the slope from the equation \( y = \frac{3}{4}x - 3 \)?
2. What would the line look like if the equation was \( 4x - 3y = 12 \)?
3. How do you graph a line using the slope and y-intercept?
4. What is the significance of the points where the line intersects the axes?
5. How would you graph the equation if it was written in standard form?
6. What happens to the graph if the coefficient of \( x \) changes?
7. How can you check if a point lies on the line?
8. How do you find the equation of a line parallel to \( 3x - 4y = 12 \)?

**Tip:** When graphing a linear equation, using the intercepts (where the line crosses the axes) is often the quickest way to find points and draw the line.

Learn how to graph the linear equation 3x - 4y = 12 by converting it into slope-intercept form and identifying two points to plot on the graph. This problem covers concepts of linear equations and graphing, suitable for Grades 7-9 students.

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