https://file.aiquickdraw.com/mathbot/file/1725368675863msbg32pc.jpg

Let's solve the problem step by step.

### Part (a) Complete the Table:

You are given the equation:

\[
2x - 5y = 10
\]

And a table with `x = 0` and `y = 0`. We need to find the corresponding `y` when `x = 0` and the corresponding `x` when `y = 0`.

1. **When \( x = 0 \):**
   \[
   2(0) - 5y = 10 \implies -5y = 10 \implies y = \frac{10}{-5} = -2
   \]
   So, when \( x = 0 \), \( y = -2 \).

2. **When \( y = 0 \):**
   \[
   2x - 5(0) = 10 \implies 2x = 10 \implies x = \frac{10}{2} = 5
   \]
   So, when \( y = 0 \), \( x = 5 \).

The completed table should be:

| x | y  |
|---|----|
| 0 | -2 |
| 5 |  0 |

### Part (b) Plot the Two Points on the Graph:

Now, let's plot the points \((0, -2)\) and \((5, 0)\) on the provided graph.

- The point \((0, -2)\) is on the y-axis at \(y = -2\).
- The point \((5, 0)\) is on the x-axis at \(x = 5\).

On the graph:
- Mark the point \((0, -2)\).
- Mark the point \((5, 0)\).

Once these points are marked, draw a straight line through them to represent the equation \(2x - 5y = 10\).

Would you like further details on any part of this solution or any specific questions?

---

### 5 Follow-up Questions:
1. How would you find the slope of the line from the equation \(2x - 5y = 10\)?
2. What are the x-intercept and y-intercept of the line, and how do they relate to the points plotted?
3. How could you rearrange the equation \(2x - 5y = 10\) into slope-intercept form \(y = mx + b\)?
4. What does the slope tell you about the relationship between \(x\) and \(y\) in the equation?
5. How would you check if another point lies on the line \(2x - 5y = 10\)?

### Tip:
To quickly find intercepts, set \(y = 0\) for the x-intercept and \(x = 0\) for the y-intercept when dealing with linear equations.

Given the linear equation 2x - 5y = 10, complete the table with values for x and y, then plot the points on a graph.

Learn how to complete a table with values for x and y and plot the points on a graph based on the linear equation 2x - 5y = 10. This problem is suitable for students in Grades 6-8, covering key concepts in linear equations and coordinate geometry.

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