Question

Which equations contain the point (0.5, -6.75)? Check the two that apply.(2 points)
Responses

2y=x+13
2 y is equal to x plus 13

2x+4y=−26
2 x plus 4 y is equal to negative 26

y=x−7.5
y is equal to x minus 7 point 5

y=0.5x−7

Answer 1

To determine which equations contain the point (0.5, -6.75), we will substitute \(x = 0.5\) and \(y = -6.75\) into each equation and check if the equations hold true.

1. **Equation:** \(2y = x + 13\)

Substitute \(x = 0.5\) and \(y = -6.75\):

\[
2(-6.75) = 0.5 + 13 \\
-13.5 = 0.5 + 13 \\
-13.5 = 13.5 \quad (\text{False})
\]

2. **Equation:** \(2x + 4y = -26\)

Substitute \(x = 0.5\) and \(y = -6.75\):

\[
2(0.5) + 4(-6.75) = -26 \\
1 - 27 = -26 \\
-26 = -26 \quad (\text{True})
\]

3. **Equation:** \(y = x - 7.5\)

Substitute \(x = 0.5\) and \(y = -6.75\):

\[
-6.75 = 0.5 - 7.5 \\
-6.75 = -7 \quad (\text{False})
\]

4. **Equation:** \(y = 0.5x - 7\)

Substitute \(x = 0.5\) and \(y = -6.75\):

\[
-6.75 = 0.5(0.5) - 7 \\
-6.75 = 0.25 - 7 \\
-6.75 = -6.75 \quad (\text{True})
\]

The equations that contain the point (0.5, -6.75) are:

- \(2x + 4y = -26\)
- \(y = 0.5x - 7\)

Thus, the correct responses are:

- **2x + 4y = -26**
- **y = 0.5x - 7**