Question

Use the information to answer the question.

The equation y = 30x represents the distance, y, in miles, a domestic cat can run after hours. The table shows the distance, y, in miles, a domestic dog can run after x
hours.
Time(in hours)
0.5
1
2
Distance(in miles)
17.5
35
70
Part A
Based on this information, which statement is true?

1.The cat and dog run the same distance every hour

2.The cat runs more miles per hour than the dog

3.The distances the dog and cat run every hour cannot be compared.

4.The dog runs more miles per hour than the cat
.

Answer 1

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Explanation:

Answer 2

Based on this information, a statement that is true is: 4.The dog runs more miles per hour than the cat.

In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:

y = kx

Where:

• y represents the y-variable or distance (miles).
• x represents the x-variable or time (hours)​.
• k is the constant of proportionality.

Next, we would determine the constant of proportionality (k) by using various data points in the table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 17.5/0.5 = 35/1 = 70/2

Constant of proportionality, k = 35

Therefore, the required linear equation for the domestic dog is given by;

y = kx

y = 35x.

Difference = 35 - 30

Difference = 5 miles per hour.

In this context, we can logically deduce that the dog runs 5 miles per hour more than the cat.