Question

Table of Values
x ya yb
0 0 3
1 2 3.5
2 4 4

Which of the following systems of linear equations does the table of values represent?

A: { y= 2x + 3
{ y = 1/2x

B: { y = 2x
{ y = 1/2x + 3

C: { y= 1/2x
{y= 2x + 3

D: { y = 2x
{ y = 3x + 1/2

Answer 1

To determine which system of linear equations the table of values represents, we can analyze the two sets of \( y \) values provided (\( y_a \) and \( y_b \)) and find the equations that fit them based on the values of \( x \).

### Analyzing \( y_a \)

Let's look at \( y_a \):
- When \( x = 0 \), \( y_a = 0 \)
- When \( x = 1 \), \( y_a = 2 \)
- When \( x = 2 \), \( y_a = 4 \)

From this, we can observe that as \( x \) increases by 1, \( y_a \) increases by 2. This suggests a linear relationship of the form:

\[
y_a = 2x
\]

### Analyzing \( y_b \)

Now, let's evaluate \( y_b \):
- When \( x = 0 \), \( y_b = 3 \)
- When \( x = 1 \), \( y_b = 3.5 \)
- When \( x = 2 \), \( y_b = 4 \)

Here, as \( x \) increases by 1, \( y_b \) increases by 0.5. This suggests a linear relationship of the form:

\[
y_b = \frac{1}{2}x + 3
\]

### Conclusion

Upon reviewing the derived equations, we have:
- For \( y_a \): \( y = 2x \)
- For \( y_b \): \( y = \frac{1}{2}x + 3 \)

This matches with option **B**:

\[
\text{B: } \{ y = 2x \\
\{ y = \frac{1}{2}x + 3 \}
\]

Thus, the correct answer is **B**.