https://file.aiquickdraw.com/mathbot/file/1722225178249rixmj7k0.png

To find the x- and y-intercepts of the line given by the equation \(7x + 2y = 14\), we can follow these steps:

### Finding the x-intercept:
The x-intercept occurs when \(y = 0\).

1. Substitute \(y = 0\) into the equation \(7x + 2y = 14\):
   \[
   7x + 2(0) = 14
   \]
   \[
   7x = 14
   \]
   \[
   x = \frac{14}{7}
   \]
   \[
   x = 2
   \]

So, the x-intercept is \((2, 0)\).

### Finding the y-intercept:
The y-intercept occurs when \(x = 0\).

1. Substitute \(x = 0\) into the equation \(7x + 2y = 14\):
   \[
   7(0) + 2y = 14
   \]
   \[
   2y = 14
   \]
   \[
   y = \frac{14}{2}
   \]
   \[
   y = 7
   \]

So, the y-intercept is \((0, 7)\).

### Plotting the Line:
Now, we can use these intercepts to sketch the graph. 

1. Plot the x-intercept \((2, 0)\) on the graph.
2. Plot the y-intercept \((0, 7)\) on the graph.
3. Draw a straight line through these two points.

### Summary
- x-intercept: \((2, 0)\)
- y-intercept: \((0, 7)\)

Let’s sketch the graph on the provided grid.

![Line Graph](attachment:image-2024-07-29-17-31-43.png)

This plot shows a straight line passing through the intercept points \((2, 0)\) and \((0, 7)\).

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Do you want more details or have any questions?

Here are 8 related questions to further explore the topic:

1. What is the slope of the line \(7x + 2y = 14\)?
2. How can we rewrite the equation \(7x + 2y = 14\) in slope-intercept form?
3. What are the coordinates of a point that lies on the line besides the intercepts?
4. How would the intercepts change if the equation were \(7x + 2y = 20\)?
5. How can we find the x- and y-intercepts for the line \(3x - 4y = 12\)?
6. What is the significance of intercepts in graphing linear equations?
7. How can you determine if two lines are parallel by looking at their equations?
8. How would the graph change if we doubled all the coefficients in the equation to \(14x + 4y = 28\)?

**Tip:** Always verify your intercept points by substituting back into the original equation to ensure they satisfy the equation.

Learn how to find the x-intercept and y-intercept of the line 7x + 2y = 14 with a detailed step-by-step solution. This problem covers linear equations and intercepts. Suitable for students in Grades 7-9.

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