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 y
150 300
250 500
360 720
480 960
f( x) = x + 150
f( x) = 2 x
f( x) = 2 x - 100
f( x) =
Answers
GPT-4o mini
To determine which equation best represents the relationship between \( x \) and \( y \) based on the provided table of values, let's start by analyzing the data.
We have the following pairs of \( (x, y) \):
- For \( x = 150, y = 300 \)
- For \( x = 250, y = 500 \)
- For \( x = 360, y = 720 \)
- For \( x = 480, y = 960 \)
To find an equation that fits these values, we first look at the relationship between \( x \) and \( y \). A common approach is to see how \( y \) relates to \( x \).
### Observing the pattern:
1. For \( x = 150, y = 300 \):
\[
y = 2 \times 150 = 300
\]
2. For \( x = 250, y = 500 \):
\[
y = 2 \times 250 = 500
\]
3. For \( x = 360, y = 720 \):
\[
y = 2 \times 360 = 720
\]
4. For \( x = 480, y = 960 \):
\[
y = 2 \times 480 = 960
\]
From the calculations above, we see that in each case, \( y \) is exactly double \( x \).
### Conclusion:
This suggests that the best fitting equation from the options given is:
\[
f(x) = 2x
\]
### Verifying against options:
- \( f(x) = x + 150 \): This does not fit as it would not yield \( y \) values that match the table.
- \( f(x) = 2x \): This fits our derived relationship as shown in the calculations.
- \( f(x) = 2x - 100 \): This also does not fit since the \( y \) values would be lower than expected.
Therefore, **the best equation that represents the information in the table is**:
\[
f(x) = 2x
\]
We have the following pairs of \( (x, y) \):
- For \( x = 150, y = 300 \)
- For \( x = 250, y = 500 \)
- For \( x = 360, y = 720 \)
- For \( x = 480, y = 960 \)
To find an equation that fits these values, we first look at the relationship between \( x \) and \( y \). A common approach is to see how \( y \) relates to \( x \).
### Observing the pattern:
1. For \( x = 150, y = 300 \):
\[
y = 2 \times 150 = 300
\]
2. For \( x = 250, y = 500 \):
\[
y = 2 \times 250 = 500
\]
3. For \( x = 360, y = 720 \):
\[
y = 2 \times 360 = 720
\]
4. For \( x = 480, y = 960 \):
\[
y = 2 \times 480 = 960
\]
From the calculations above, we see that in each case, \( y \) is exactly double \( x \).
### Conclusion:
This suggests that the best fitting equation from the options given is:
\[
f(x) = 2x
\]
### Verifying against options:
- \( f(x) = x + 150 \): This does not fit as it would not yield \( y \) values that match the table.
- \( f(x) = 2x \): This fits our derived relationship as shown in the calculations.
- \( f(x) = 2x - 100 \): This also does not fit since the \( y \) values would be lower than expected.
Therefore, **the best equation that represents the information in the table is**:
\[
f(x) = 2x
\]