(a) y = 4x is in direct proportion. If x increases, y also increases by a constant factor of 4, and if x decreases, y also decreases by a constant factor of 4. This is the definition of direct proportion.
(b) y = x + 2 is not in direct proportion. If x increases, y also increases, but not by a constant factor, and if x decreases, y also decreases, but not by a constant factor. The relationship between x and y is linear, but not directly proportional.
(c) y = x² is not in direct proportion. If x increases, y also increases, but not by a constant factor, and if x decreases, y also decreases, but not by a constant factor. The relationship between x and y is non-linear, and not directly proportional.
(d) y = 1/2x is in direct proportion. If x increases, y increases by a constant factor of 1/2, and if x decreases, y decreases by a constant factor of 1/2. This is the definition of direct proportion.
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Step-by-step explanation:
(a) y = 4x is in direct proportion. If x increases, y also increases by a constant factor of 4, and if x decreases, y also decreases by a constant factor of 4. This is the definition of direct proportion.
(b) y = x + 2 is not in direct proportion. If x increases, y also increases, but not by a constant factor, and if x decreases, y also decreases, but not by a constant factor. The relationship between x and y is linear, but not directly proportional.
(c) y = x² is not in direct proportion. If x increases, y also increases, but not by a constant factor, and if x decreases, y also decreases, but not by a constant factor. The relationship between x and y is non-linear, and not directly proportional.
(d) y = 1/2x is in direct proportion. If x increases, y increases by a constant factor of 1/2, and if x decreases, y decreases by a constant factor of 1/2. This is the definition of direct proportion.
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