Question

Given the table of values below, which equation best represents the information?

x y
150 300
250 500
360 720
480 960
f( x) = x + 150
f( x) = 2 x
f( x) = 2 x - 100
f( x) = x/2

Answer 1

To determine which equation best represents the relationship between \( x \) and \( y \) given in the table, we can evaluate each equation with the provided \( x \) values and check if the outcomes match the corresponding \( y \) values.

The equations provided are:

1. \( f(x) = x + 150 \)
2. \( f(x) = 2x \)
3. \( f(x) = 2x - 100 \)
4. \( f(x) = \frac{x}{2} \)

Let's evaluate each equation with the given values of \( x \):

1. **For \( f(x) = x + 150 \)**:
- When \( x = 150 \), \( f(150) = 150 + 150 = 300 \) (matches)
- When \( x = 250 \), \( f(250) = 250 + 150 = 400 \) (does not match)
- This equation does not fit for all \( x \).

2. **For \( f(x) = 2x \)**:
- When \( x = 150 \), \( f(150) = 2(150) = 300 \) (matches)
- When \( x = 250 \), \( f(250) = 2(250) = 500 \) (matches)
- When \( x = 360 \), \( f(360) = 2(360) = 720 \) (matches)
- When \( x = 480 \), \( f(480) = 2(480) = 960 \) (matches)
- This equation fits all \( x \).

3. **For \( f(x) = 2x - 100 \)**:
- When \( x = 150 \), \( f(150) = 2(150) - 100 = 300 - 100 = 200 \) (does not match)
- This equation does not fit for all \( x \).

4. **For \( f(x) = \frac{x}{2} \)**:
- When \( x = 150 \), \( f(150) = \frac{150}{2} = 75 \) (does not match)
- This equation does not fit for all \( x \).

Based on the evaluations, the only equation that consistently matches the \( x \) and \( y \) values in the table is:

**\( f(x) = 2x \)**.