Question

The graph shows the number of jam jars filled by two different machines over several minutes.


The equation y = 3x represents the number of jars, y, Machine A fills in x min.



Which equation could represent the number of jars filled by Machine B?

Responses

y = 1.5x
y = 1.5 x

y = 3x
y = 3 x

y = 6x
y = 6 x

y = 8x
y = 8 x
A graph measuring number of jars and time. Two lines, labeled Machine A and Machine B, exit the origin to show that distance increases as time increases

Answer 1

To determine which equation could represent the number of jars filled by Machine B, we need to consider the comparison with Machine A's equation, which is \( y = 3x \). This means Machine A fills 3 jars per minute.

Next, we need to analyze the options based on potential rates of jar filling relative to Machine A. The options given are:

1. \( y = 1.5x \)
2. \( y = 3x \)
3. \( y = 6x \)
4. \( y = 8x \)

- **\( y = 1.5x \)**: This indicates that Machine B fills 1.5 jars per minute, which is a lower rate than Machine A.
- **\( y = 3x \)**: This suggests that Machine B and Machine A fill jars at the same rate.
- **\( y = 6x \)**: This indicates that Machine B fills 6 jars per minute, which is a higher rate than Machine A.
- **\( y = 8x \)**: This indicates that Machine B fills 8 jars per minute, also a higher rate than Machine A.

To choose the correct representation for Machine B, we would typically look at the graph and see if Machine B's line is above, below, or parallel to Machine A's line.

If Machine B filled more jars than Machine A, the correct equation should reflect a greater rate than 3 jars per minute. Conversely, if Machine B is not as efficient, it would have a rate lower than 3 jars per minute.

Since I don't have the visual of the graph, I can’t definitively determine which equation corresponds to Machine B without that context. However, typically, if Machine B is performing better, you would choose \( y = 6x \) or \( y = 8x \). If it is less efficient, you would choose \( y = 1.5x \).

Please refer to the graph to see if Machine B's line is above, below, or aligns with Machine A's to decide which equation fits best.