Plot the points A(2, 4) and B(4, 2) on a graph sheet and draw a line passing through these two points. Extend the line on both sides to meet the coordinate axes. What are the coordinates of the points where this line meets the x-axis and the y-axis?

Answer

To solve the problem of plotting the points A(2, 4) and B(4, 2) on a graph sheet, drawing a line through these points, and finding where this line intersects the x-axis and y-axis, follow these steps:

### Step-by-Step Solution:

1. **Draw the Axes**:
- Start by drawing the x-axis (horizontal line) and the y-axis (vertical line) on your graph sheet. Label the origin (0, 0) where the two axes intersect.

**Hint**: Make sure to extend both axes enough to accommodate the points you will plot.

2. **Label the Axes**:
- Mark the positive values on both axes. For the x-axis, mark points from 0 to at least 5 (0, 1, 2, 3, 4, 5) and for the y-axis, mark points from 0 to at least 5 (0, 1, 2, 3, 4, 5).

**Hint**: Since both points A and B have positive coordinates, you don’t need to mark negative values.

3. **Plot Point A(2, 4)**:
- To plot point A, start at the origin (0, 0). Move 2 units to the right along the x-axis (to 2) and then move 4 units up along the y-axis (to 4). Mark this point and label it as A.

**Hint**: The first coordinate (2) corresponds to the x-axis, and the second coordinate (4) corresponds to the y-axis.

4. **Plot Point B(4, 2)**:
- For point B, again start at the origin (0, 0). Move 4 units to the right along the x-axis (to 4) and then move 2 units up along the y-axis (to 2). Mark this point and label it as B.

**Hint**: Remember to check your movements on both axes carefully to ensure accuracy.

5. **Draw the Line**:
- Use a ruler to draw a straight line connecting points A and B. Extend this line on both sides beyond points A and B.

**Hint**: Make sure the line is straight and extends far enough to intersect the axes clearly.

6. **Find the Intersection with the Y-axis**:
- To find where the line intersects the y-axis, look for the point where the line crosses the y-axis (where x = 0).

**Hint**: You can visually inspect the graph or use the equation of the line if needed.

7. **Find the Intersection with the X-axis**:
- To find where the line intersects the x-axis, look for the point where the line crosses the x-axis (where y = 0).

**Hint**: Again, you can visually inspect the graph or use the equation of the line if needed.

8. **Record the Coordinates**:
- The coordinates where the line meets the y-axis will be (0, 6) and where it meets the x-axis will be (6, 0).

**Hint**: Make sure to write down the coordinates clearly.

### Final Answer:
- The coordinates where the line meets the x-axis are (6, 0).
- The coordinates where the line meets the y-axis are (0, 6).