Find the​ x-intercept and the​ y-intercept of the graph of the equation.
6 x plus 4 y equals 72

To find the x-intercept and y-intercept of the equation \( 6x + 4y = 72 \), we follow these steps:

### 1. **Finding the x-intercept:**

At the x-intercept, the value of \( y = 0 \). So, we substitute \( y = 0 \) into the equation and solve for \( x \):

\[
6x + 4(0) = 72
\]
\[
6x = 72
\]
\[
x = \frac{72}{6} = 12
\]

So, the x-intercept is \( (12, 0) \).

### 2. **Finding the y-intercept:**

At the y-intercept, the value of \( x = 0 \). So, we substitute \( x = 0 \) into the equation and solve for \( y \):

\[
6(0) + 4y = 72
\]
\[
4y = 72
\]
\[
y = \frac{72}{4} = 18
\]

So, the y-intercept is \( (0, 18) \).

### Final Answer:
- The x-intercept is \( (12, 0) \).
- The y-intercept is \( (0, 18) \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you plot these intercepts on a graph?
2. What would happen if the equation was \( 6x + 4y = 0 \)?
3. How do intercepts help in graphing linear equations?
4. Can you rewrite this equation in slope-intercept form?
5. How would the intercepts change if the equation were \( 6x - 4y = 72 \)?

**Tip:** Always remember, the x-intercept is where \( y = 0 \) and the y-intercept is where \( x = 0 \).

Find the​ x-intercept and the​ y-intercept of the graph of the equation 6x + 4y = 72.

Learn how to find the x-intercept and y-intercept of the linear equation 6x + 4y = 72. This step-by-step guide covers essential algebraic concepts, perfect for students in Grades 7-10.

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