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:

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.