Question

The equation yequalsseven halves
x describes the number of inches y that a snail travels in x minutes. How does y change as x​ changes? Describe what the change means in this situation.
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Part 1
Choose the correct answer below.
A.
As x increases by 2​, y increases by 7. This means that every 7 minutes the snail travels 2 inches.
B.
As x increases by 7​, y increases by 2. This means that every 2 minutes the snail travels 7 inches.
C.
As x increases by 2​, y increases by 7. This means that every 2 minutes the snail travels 7 inches.
D.
As x increases by 7​, y increases by 2. This means that every 7 minutes the snail travels 2 inches.

Answer 1

The equation \( y = \frac{7}{2} x \) indicates that for every increase in \( x \) (the number of minutes), \( y \) (the number of inches the snail travels) changes proportionally.

To understand the relationship, we can determine how much \( y \) increases when \( x \) increases by 2:

1. When \( x \) increases by 2, substitute into the equation:
\[
y = \frac{7}{2} (x + 2) = \frac{7}{2} x + \frac{7}{2} \times 2 = \frac{7}{2} x + 7
\]
This shows that \( y \) increases by 7.

Therefore, the correct interpretation of the relationship is:

**Option C**: As \( x \) increases by 2, \( y \) increases by 7. This means that every 2 minutes the snail travels 7 inches.

So the answer is **C**.