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 4
a proportional linear equation with the slope of 4

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

a proportional linear equation with the slope of −14

Answer 1

A proportional linear equation can be represented in the form \( y = mx \), where \( m \) is the slope. To determine which equation contains the ordered pair \((-2, -0.5)\), we can plug in the x-value (-2) into each equation in order to check if we can get the y-value (-0.5).

1. For the slope of 4:
\[
y = 4(-2) = -8 \quad (\text{not } -0.5)
\]

2. For the slope of 14:
\[
y = 14(-2) = -28 \quad (\text{not } -0.5)
\]

3. For the slope of \(\frac{1}{4}\):
\[
y = \frac{1}{4}(-2) = -\frac{1}{2} = -0.5 \quad (\text{this works!})
\]

4. For the slope of -4:
\[
y = -4(-2) = 8 \quad (\text{not } -0.5)
\]

5. For the slope of -14:
\[
y = -14(-2) = 28 \quad (\text{not } -0.5)
\]

The ordered pair \((-2, -0.5)\) is contained in the proportional linear equation with the slope of \(\frac{1}{4}\).