Question

The graph represents y=1/4x+1/2
Which ordered pairs represents a point on the line and solutions to the equation? Select all that apply.

(3,1)
(-2,0)
(0,0.5)
(2,1)
(0,-2)
(6,2)

Answer 1

To determine which ordered pairs are solutions to the equation \( y = \frac{1}{4}x + \frac{1}{2} \), we can substitute the \( x \) value of each ordered pair into the equation and see if the resulting \( y \) value matches the \( y \) value of the ordered pair.

1. For \( (3, 1) \):
\[
y = \frac{1}{4}(3) + \frac{1}{2} = \frac{3}{4} + \frac{1}{2} = \frac{3}{4} + \frac{2}{4} = \frac{5}{4} \quad \text{(not a solution)}
\]

2. For \( (-2, 0) \):
\[
y = \frac{1}{4}(-2) + \frac{1}{2} = -\frac{1}{2} + \frac{1}{2} = 0 \quad \text{(is a solution)}
\]

3. For \( (0, 0.5) \):
\[
y = \frac{1}{4}(0) + \frac{1}{2} = 0 + \frac{1}{2} = 0.5 \quad \text{(is a solution)}
\]

4. For \( (2, 1) \):
\[
y = \frac{1}{4}(2) + \frac{1}{2} = \frac{1}{2} + \frac{1}{2} = 1 \quad \text{(is a solution)}
\]

5. For \( (0, -2) \):
\[
y = \frac{1}{4}(0) + \frac{1}{2} = 0 + \frac{1}{2} = 0.5 \quad \text{(not a solution)}
\]

6. For \( (6, 2) \):
\[
y = \frac{1}{4}(6) + \frac{1}{2} = \frac{3}{2} + \frac{1}{2} = 2 \quad \text{(is a solution)}
\]

From this analysis, the ordered pairs that are solutions to the equation are:

- \((-2, 0)\)
- \((0, 0.5)\)
- \((2, 1)\)
- \((6, 2)\)

Thus, the final answer includes the ordered pairs:
- \((-2, 0)\)
- \((0, 0.5)\)
- \((2, 1)\)
- \((6, 2)\)