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The table below represents the relationship between the distance a car travels (y) in miles, and the time (x) in minutes.

| Time (x) | Distance (y) |
|----------|--------------|
| 48 | 12 |
| 64 | 16 |
| 72 | 18 |

Which equation represents the relationship between distance and time for this car?

A. [tex]\( y = \frac{1}{4}x \)[/tex]

B. [tex]\( x = \frac{1}{3}y \)[/tex]

C. [tex]\( y = 48x \)[/tex]



Answer :

GinnyAnswer
To determine which equation represents the relationship between the distance a car travels, [tex]\(y\)[/tex], in miles, and the time [tex]\(x\)[/tex], in minutes, we'll analyze the data given in the table:

[tex]\[ \begin{array}{|c|c|} \hline \text{Time, } x & \text{Distance, } y \\ \hline 48 & 12 \\ 64 & 16 \\ 72 & 18 \\ \hline \end{array} \][/tex]

First, we calculate the ratio [tex]\( \frac{y}{x} \)[/tex] for each pair of values:

1. For [tex]\(x = 48\)[/tex] and [tex]\(y = 12\)[/tex]:
[tex]\[ \frac{y}{x} = \frac{12}{48} = \frac{1}{4} \][/tex]

2. For [tex]\(x = 64\)[/tex] and [tex]\(y = 16\)[/tex]:
[tex]\[ \frac{y}{x} = \frac{16}{64} = \frac{1}{4} \][/tex]

3. For [tex]\(x = 72\)[/tex] and [tex]\(y = 18\)[/tex]:
[tex]\[ \frac{y}{x} = \frac{18}{72} = \frac{1}{4} \][/tex]

We observe that the ratio [tex]\( \frac{y}{x} \)[/tex] is consistent for all data points and equals [tex]\( \frac{1}{4} \)[/tex]. This implies a linear relationship between [tex]\(y\)[/tex] and [tex]\(x\)[/tex] and can be expressed as:

[tex]\[ y = \frac{1}{4} x \][/tex]

Therefore, the equation that represents the relationship between the distance [tex]\(y\)[/tex] and the time [tex]\(x\)[/tex] for the car is:

[tex]\[ y = \frac{1}{4} x \][/tex]

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