Question

Graphing Equations Quick Check
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Question
Decide which of the following equations represents a proportional relationship.(1 point)
Responses

y=3x+1
y equals 3 x plus 1

y=13x
y equals Start Fraction 1 over 3 End Fraction x

y=x3−3
y equals Start Fraction x over 3 End Fraction minus 3

y=x+3

Answer 1

A proportional relationship can be identified by the equation having the form \( y = kx \), where \( k \) is a constant. This means that when \( x \) is 0, \( y \) must also equal 0, which indicates that the graph passes through the origin (0,0).

Now, let's analyze the given equations:

1. **\( y = 3x + 1 \)**: This is not proportional because it does not pass through the origin. When \( x = 0 \), \( y = 1 \).

2. **\( y = \frac{1}{3} x \)**: This is a proportional relationship since it can be rewritten as \( y = kx \) with \( k = \frac{1}{3} \). It passes through the origin.

3. **\( y = x^3 - 3 \)**: This is not proportional because it does not pass through the origin. When \( x = 0 \), \( y = -3 \).

4. **\( y = x + 3 \)**: This is not proportional because it does not pass through the origin. When \( x = 0 \), \( y = 3 \).

Based on the analysis above, the equation that represents a proportional relationship is:

**\( y = \frac{1}{3} x \)**.