Question

Which of the following proportional linear equations has a graph that contains the ordered pair (−2,−0.5)
?(1 point)
Responses

a proportional linear equation with the slope of 14
a proportional linear equation with the slope of Start Fraction 1 over 4 End Fraction

a proportional linear equation with the slope of −14
a proportional linear equation with the slope of negative Start Fraction 1 over 4 End Fraction

a proportional linear equation with the slope of −4
a proportional linear equation with the slope of negative 4

a proportional linear equation with the slope of 4

Answer 1

To determine which proportional linear equation has a graph that contains the ordered pair (−2, −0.5), we can use the format of a proportional equation, which is \( y = mx \), where \( m \) is the slope.

We can check each option by substituting \( x = -2 \) into the equations based on their respective slopes and seeing if we get \( y = -0.5 \).

1. **Slope of 14**:
\[
y = 14(-2) = -28 \quad \text{(does not equal -0.5)}
\]

2. **Slope of \( \frac{1}{4} \)**:
\[
y = \frac{1}{4}(-2) = -\frac{2}{4} = -0.5 \quad \text{(equals -0.5)}
\]

3. **Slope of −14**:
\[
y = -14(-2) = 28 \quad \text{(does not equal -0.5)}
\]

4. **Slope of \(-\frac{1}{4}\)**:
\[
y = -\frac{1}{4}(-2) = \frac{2}{4} = 0.5 \quad \text{(does not equal -0.5)}
\]

5. **Slope of −4**:
\[
y = -4(-2) = 8 \quad \text{(does not equal -0.5)}
\]

6. **Slope of 4**:
\[
y = 4(-2) = -8 \quad \text{(does not equal -0.5)}
\]

From the calculations, the only slope that gives the ordered pair (−2, −0.5) is the proportional linear equation with a slope of \( \frac{1}{4} \).

**Answer: a proportional linear equation with the slope of \( \frac{1}{4} \)**.