Questions: SLOPE 0 20 2 15 Y -INTERCEPT 2 / 3 Equation Proportional or Not Proportional y=2 / 3(x)+3 y=2 x+20 y=20(x) y=-5(x)+1 / 2 Proportional Non Proportional

Solution Steps

To solve the given problem, we need to determine whether each of the provided equations represents a proportional relationship or a non-proportional relationship. A proportional relationship is one where the equation can be written in the form \( y = kx \), where \( k \) is a constant. If there is an additional constant term (y-intercept) other than zero, the relationship is non-proportional.

We have the following equations to analyze for proportionality:

1. \( y = \frac{2}{3}(x) + 3 \)
2. \( y = 2x + 20 \)
3. \( y = 20(x) \)
4. \( y = -5(x) + \frac{1}{2} \)

A relationship is proportional if it can be expressed in the form \( y = kx \) where \( k \) is a constant. If there is an additional constant term (y-intercept) other than zero, the relationship is non-proportional.

• For \( y = \frac{2}{3}(x) + 3 \): The presence of the constant \( 3 \) indicates it is Non Proportional.
• For \( y = 2x + 20 \): The presence of the constant \( 20 \) indicates it is Non Proportional.
• For \( y = 20(x) \): This can be expressed as \( y = 20x \), indicating it is Proportional.
• For \( y = -5(x) + \frac{1}{2} \): The presence of the constant \( \frac{1}{2} \) indicates it is Non Proportional.

Based on the analysis:

• \( y = \frac{2}{3}(x) + 3 \): Non Proportional
• \( y = 2x + 20 \): Non Proportional
• \( y = 20(x) \): Proportional
• \( y = -5(x) + \frac{1}{2} \): Non Proportional

Final Answer