If (p(x)=mx+n), (p(2)=9) and (p(5)=21), what is (m)?
Answer and explanation
Correct answer: \(4\)
Given \(p(x)=mx+n\), we have \(p(2)=2m+n=9\) and \(p(5)=5m+n=21\). Subtracting the first equation from the second gives \(3m=12\), so \(m=4\). The constant term \(n\) cancels because it is the same in both equations. Exam tip: When two values of a linear polynomial are given, subtract the equations to find \(m\) first.
Frequently asked questions
What is the correct answer to this question?
\(4\)
Why is this the correct answer?
Given \(p(x)=mx+n\), we have \(p(2)=2m+n=9\) and \(p(5)=5m+n=21\). Subtracting the first equation from the second gives \(3m=12\), so \(m=4\). The constant term \(n\) cancels because it is the same in both equations. Exam tip: When two values of a linear polynomial are given, subtract the equations to find \(m\) first.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear polynomials.
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