Asked by Rose
why does the equation y = 3x + 5 not represent a proportional relationship.
explain in an 7th graders words
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GPT-5 mini
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A proportional relationship means y grows exactly in step with x and the line goes through the origin (0,0). In equations, that looks like y = kx (no extra number added), and the ratio y/x is always the same number k.
y = 3x + 5 is not proportional because of the +5.
- If x = 0, y = 3·0 + 5 = 5. A proportional line would give y = 0 when x = 0.
- Also check the ratios: for x = 1, y = 8 so y/x = 8. For x = 2, y = 11 so y/x = 11/2 = 5.5. These ratios are different, so y/x is not constant.
Think of it this way: y = 3x is like getting $3 for every hour you work (no start money). y = 3x + 5 is like getting a $5 sign-up bonus plus $3 each hour. Because of that bonus, it’s not a proportional relationship.
y = 3x + 5 is not proportional because of the +5.
- If x = 0, y = 3·0 + 5 = 5. A proportional line would give y = 0 when x = 0.
- Also check the ratios: for x = 1, y = 8 so y/x = 8. For x = 2, y = 11 so y/x = 11/2 = 5.5. These ratios are different, so y/x is not constant.
Think of it this way: y = 3x is like getting $3 for every hour you work (no start money). y = 3x + 5 is like getting a $5 sign-up bonus plus $3 each hour. Because of that bonus, it’s not a proportional relationship.
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