Question

POSSIBLE POINTS: 3.13


Which equation matches this table?
Responses

y = 2x
y = 2x

y = -1/2 x
y = -1/2 x

y = 1/2 x
y = 1/2 x

y = -2x + 1
y = -2x + 1

y = x + 2
y = x + 2

y = 1/2 x + 2




# of mule:2,4,6,8,10
bales of hay:1,2,3,4,5

Answer 1

To find which equation matches the provided table of data, we first need to analyze the values given for the number of mules and the corresponding bales of hay:

| # of Mules (x) | Bales of Hay (y) |
|----------------|-------------------|
| 2 | 1 |
| 4 | 2 |
| 6 | 3 |
| 8 | 4 |
| 10 | 5 |

We can observe that as the number of mules increases by 2, the number of bales of hay increases by 1. This suggests a linear relationship.

To derive the equation, we can find the slope of the line (m):

- The change in y (bales of hay) = 2 - 1 = 1 (for 2 mules to 4 mules)
- The change in x (number of mules) = 4 - 2 = 2

The slope \( m \) is given by:
\[
m = \frac{\Delta y}{\Delta x} = \frac{1}{2}
\]

Now we can use the slope-intercept form of the equation:
\[
y = mx + b
\]

We have found that \( m = \frac{1}{2} \). We can use one of the points to solve for \( b \). Let's use the point (2, 1):

\[
1 = \frac{1}{2}(2) + b
\]
\[
1 = 1 + b
\]
\[
b = 0
\]

Thus, the equation is:
\[
y = \frac{1}{2}x
\]

Looking at the response options provided, we see that one of them matches our derived equation:

- **\(y = \frac{1}{2}x\)**

Therefore, the correct answer is:

**y = 1/2 x**