Question

Choose all of the pairs that are included in the set of solutions for the equation
y=1/2 x+3/2
when plotted in the coordinate plane.
Responses
A (−4, −1)
B (3, 3)
C (−5, −1)
D (7, 5)
E (2, 3)

Answer 1

To determine which pairs are solutions to the equation \(y = \frac{1}{2} x + \frac{3}{2}\), we can substitute the x-values from each pair into the equation and see if we obtain the corresponding y-values.

1. **For A (−4, −1)**:
\[
y = \frac{1}{2}(-4) + \frac{3}{2} = -2 + \frac{3}{2} = -2 + 1.5 = -0.5 \quad \text{(not } -1\text{)}
\]
This pair is not a solution.

2. **For B (3, 3)**:
\[
y = \frac{1}{2}(3) + \frac{3}{2} = \frac{3}{2} + \frac{3}{2} = 3
\]
This pair is a solution.

3. **For C (−5, −1)**:
\[
y = \frac{1}{2}(-5) + \frac{3}{2} = -\frac{5}{2} + \frac{3}{2} = -1
\]
This pair is a solution.

4. **For D (7, 5)**:
\[
y = \frac{1}{2}(7) + \frac{3}{2} = \frac{7}{2} + \frac{3}{2} = \frac{10}{2} = 5
\]
This pair is a solution.

5. **For E (2, 3)**:
\[
y = \frac{1}{2}(2) + \frac{3}{2} = 1 + \frac{3}{2} = 1 + 1.5 = 2.5 \quad \text{(not } 3\text{)}
\]
This pair is not a solution.

**Final answers** that are included in the set of solutions for the equation are:
- B (3, 3)
- C (−5, −1)
- D (7, 5)