https://file.aiquickdraw.com/mathbot/file/1726759946544lyxrag18.jpg

Let's solve the given equation step by step to address the questions in the image.

The equation provided is:

\[
4x + 7y = 28
\]

### 1. **Determine the intercepts:**
To find the **x-intercept**, set \( y = 0 \) and solve for \( x \).

\[
4x + 7(0) = 28 \implies 4x = 28 \implies x = \frac{28}{4} = 7
\]
Thus, the x-intercept is \( (7, 0) \).

To find the **y-intercept**, set \( x = 0 \) and solve for \( y \).

\[
4(0) + 7y = 28 \implies 7y = 28 \implies y = \frac{28}{7} = 4
\]
Thus, the y-intercept is \( (0, 4) \).

### 2. **Check the other points:**

Let’s see if the other points provided satisfy the equation.

- For \( (0, 7) \):
  \[
  4(0) + 7(7) = 0 + 49 = 49 \quad (\text{Not valid, since it does not equal 28}).
  \]

- For \( (4, 0) \):
  \[
  4(4) + 7(0) = 16 + 0 = 16 \quad (\text{Not valid, since it does not equal 28}).
  \]

- For \( (7, 4) \):
  \[
  4(7) + 7(4) = 28 + 28 = 56 \quad (\text{Not valid, since it does not equal 28}).
  \]

Thus, the correct intercept points are **(7, 0)** and **(0, 4)**, corresponding to the x-intercept and y-intercept.

### Summary:
- **X-intercept**: (7, 0)
- **Y-intercept**: (0, 4)

Let me know if you need further details! Here are five related questions to deepen your understanding:

1. How do you determine the slope of the line from the equation \( 4x + 7y = 28 \)?
2. How would you rewrite \( 4x + 7y = 28 \) in slope-intercept form?
3. What is the slope of a line perpendicular to the line described by \( 4x + 7y = 28 \)?
4. If you were to translate the graph of \( 4x + 7y = 28 \) upwards by 2 units, how would the equation change?
5. How would you graph the line if the equation were given in standard form \( Ax + By = C \), like \( 4x + 7y = 28 \)?

**Tip:** When solving for intercepts in linear equations, always set the other variable to 0 to simplify the process.

In Box #7, graph the equation: 4x + 7y = 28. Then answer the following question: Determine the x-intercept and y-intercept.

Learn how to graph the linear equation 4x + 7y = 28 by determining the x-intercept and y-intercept. This problem helps students practice finding intercepts using key algebraic concepts, suitable for Grades 7-9.

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