QuestionQuestion 14(Multiple Choice Worth 2 points) (Linear Relationships LC) Which linear equation shows a proportional relationship? $y=-2$ $y=3 x+1$ $y=\frac{3}{2} x$ $y=\frac{1}{2} x-3$

Studdy Solution

STEP 1

1. A proportional relationship is a specific type of linear relationship where the line passes through the origin.
2. For a linear equation to show a proportional relationship, it must be in the form $y = kx$ , where $k$ is a constant and there is no constant term added or subtracted.

STEP 2

1. Identify the form of each given linear equation.
2. Determine if each equation is in the form $y = kx$ .
3. Identify which equation represents a proportional relationship.

STEP 3

Identify the form of each given linear equation:
1. $y = -2$
2. $y = 3x + 1$
3. $y = \frac{3}{2}x$
4. $y = \frac{1}{2}x - 3$

STEP 4

Determine if each equation is in the form $y = kx$ :
1. $y = -2$ is a horizontal line and not in the form $y = kx$ .
2. $y = 3x + 1$ has a constant term $+1$ , so it is not in the form $y = kx$ .
3. $y = \frac{3}{2}x$ is in the form $y = kx$ with $k = \frac{3}{2}$ .
4. $y = \frac{1}{2}x - 3$ has a constant term $-3$ , so it is not in the form $y = kx$ .

STEP 5

Identify which equation represents a proportional relationship:
The equation $y = \frac{3}{2}x$ is the only one in the form $y = kx$ , indicating a proportional relationship.
The linear equation that shows a proportional relationship is $\boxed{y = \frac{3}{2}x}$ .

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