Question

The graph below shows the relationship between the time on the x axis , and the
distance on the y axis . Which Equation represents this relationship

A y = (2/1) x B y = x C y = ½ x D y = 4x

Answer 1

To determine which equation represents the relationship shown in the graph, we need to analyze the graph's slope and y-intercept.

1. **Identifying the Slope**: The slope of the line on a distance-time graph represents the speed. A steeper slope indicates a higher speed.

2. **Identifying the Y-Intercept**: The y-intercept represents the initial distance when time is zero. If the line passes through the origin (0,0), the y-intercept would be zero.

Given the options:

- **A: \(y = \frac{2}{1}x\)** or \(y = 2x\) (slope of 2)
- **B: \(y = x\)** (slope of 1)
- **C: \(y = \frac{1}{2}x\)** (slope of 0.5)
- **D: \(y = 4x\)** (slope of 4)

Without seeing the graph, we can reason based on typical interpretations:

- If the slope is 2, the distance increases by 2 units for every 1 unit of time (choice A).
- If the slope is 1, the distance increases by 1 unit for every 1 unit of time (choice B).
- If the slope is 0.5, the distance increases by 0.5 units for every 1 unit of time (choice C).
- If the slope is 4, the distance increases by 4 units for every 1 unit of time (choice D).

You would need to refer to the graph to identify the correct slope based on how the line rises.

- If you observe the line rising steeply, then it may correspond to choice D.
- If it rises moderately, it may be choice A or B.
- If it rises gently, it would be choice C.

So, evaluate the graph based on these slopes. If you can provide any additional clarity on the graph, I can help narrow it down more precisely!