Graphical Representation of the Paths of Two Trains
Video Explanation
Question
The path of train A is given by the equation
\[ 3x + 4y – 12 = 0 \]
and the path of another train B is given by
\[ 6x + 8y – 48 = 0. \]
Represent this situation graphically.
Solution
Step 1: Write Both Equations in Standard Form
Equation of train A:
\[ 3x + 4y = 12 \Rightarrow y = -\frac{3}{4}x + 3 \]
Equation of train B:
\[ 6x + 8y = 48 \Rightarrow 3x + 4y = 24 \Rightarrow y = -\frac{3}{4}x + 6 \]
Step 2: Prepare Table of Values
For Train A: \(3x + 4y = 12\)
| x | y |
|---|---|
| 0 | 3 |
| 4 | 0 |
For Train B: \(6x + 8y = 48\)
| x | y |
|---|---|
| 0 | 6 |
| 8 | 0 |
Step 3: Graphical Representation
Plot the points corresponding to each equation on the same graph:
- Train A: \((0,3)\) and \((4,0)\)
- Train B: \((0,6)\) and \((8,0)\)
Join each pair of points to obtain two straight lines.
Step 4: Interpretation of the Graph
Both lines have the same slope:
\[ -\frac{3}{4} \]
Hence, the two lines are parallel and do not intersect.
Conclusion
The paths of train A and train B are represented by two parallel straight lines.
This shows that the trains are moving along parallel tracks and will never meet.