Which option is non-constant and represents linear growth of y with x?
Answer and explanation
Correct answer: y = 18 + 2x
A linear relationship has the form y = a + bx, where b is the rate of change or slope. For genuine linear growth as x increases, the slope must be positive, so b > 0. In option C, y = 18 + 2x, the slope is 2; therefore y increases by 2 units whenever x increases by 1, and the expression is not constant. Option A has slope 0 and is constant. Option B is also constant because 18 + 0x always equals 18. Option D has slope −2, so it represents linear decrease rather than growth. Thus option C is uniquely correct.
Frequently asked questions
What is the correct answer to this question?
y = 18 + 2x
Why is this the correct answer?
A linear relationship has the form y = a + bx, where b is the rate of change or slope. For genuine linear growth as x increases, the slope must be positive, so b > 0. In option C, y = 18 + 2x, the slope is 2; therefore y increases by 2 units whenever x increases by 1, and the expression is not constant. Option A has slope 0 and is constant. Option B is also constant because 18 + 0x always equals 18. Option D has slope −2, so it represents linear decrease rather than growth. Thus option C is uniquely correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear growth and decay.
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