If (y=44+10x), what will be the total increase in (y) from (x=2) to (x=7)?
Answer and explanation
Correct answer: (50)
A linear expression of the form \(y=44+10x\) changes by a fixed amount whenever \(x\) changes by one unit. The coefficient of \(x\), namely 10, is the growth rate. The constant 44 is the starting value, but it does not affect the increase between two values of \(x\). Therefore, the useful idea is to multiply the change in \(x\) by the rate of change.
From \(x=2\) to \(x=7\), the change in \(x\) is \(7-2=5\). Hence the change in \(y\) is \(10\times5=50\). Equivalently, \(y(2)=64\) and \(y(7)=114\), whose difference is \(114-64=50\). Thus option B is correct. The value 44 should not be added again, because the question asks for the increase, not the final value.
Frequently asked questions
What is the correct answer to this question?
(50)
Why is this the correct answer?
A linear expression of the form \(y=44+10x\) changes by a fixed amount whenever \(x\) changes by one unit. The coefficient of \(x\), namely 10, is the growth rate. The constant 44 is the starting value, but it does not affect the increase between two values of \(x\). Therefore, the useful idea is to multiply the change in \(x\) by the rate of change.
From \(x=2\) to \(x=7\), the change in \(x\) is \(7-2=5\). Hence the change in \(y\) is \(10\times5=50\). Equivalently, \(y(2)=64\) and \(y(7)=114\), whose difference is \(114-64=50\). Thus option B is correct. The value 44 should not be added again, because the question asks for the increase, not the final value.
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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