Represent the situation graphically

Video Explanation

Watch the video explanation below:

Given

The path of train A is given by:

3x + 4y − 12 = 0

The path of train B is given by:

6x + 8y − 48 = 0

To Represent

The given situation graphically.

Solution

Step 1: Write Both Equations in Standard Form

Equation of train A:

3x + 4y = 12   …(1)

Equation of train B:

6x + 8y = 48

Dividing equation (2) by 2:

3x + 4y = 24   …(2)

Step 2: Prepare Tables of Values

For Equation (1): 3x + 4y = 12

If x = 0, then y = 3

If y = 0, then x = 4

Points: (0, 3) and (4, 0)

For Equation (2): 3x + 4y = 24

If x = 0, then y = 6

If y = 0, then x = 8

Points: (0, 6) and (8, 0)

Step 3: Draw the Graph

• Draw X-axis and Y-axis on graph paper.
• Plot the points (0, 3) and (4, 0) and join them to get the graph of equation (1).
• Plot the points (0, 6) and (8, 0) and join them to get the graph of equation (2).

Observation

The two lines do not intersect and are parallel to each other.

Conclusion

Since the paths of the two trains are represented by parallel straight lines, the trains will never meet.