If a quantity starts at (66) and decreases by (3) each step, which rule represents it?
Answer and explanation
Correct answer: \(y=66-3x\)
A linear rule has the form \(y=a+mx\), where \(a\) is the initial value and \(m\) is the change per step. Here, the initial value is 66 and the quantity decreases by 3 each step, so \(m=-3\). Therefore, the rule is \(y=66-3x\). The rule \(y=66+3x\) represents an increase of 3 per step, so it is not correct. Exam tip: the phrase “decreases by” indicates a negative slope.
Frequently asked questions
What is the correct answer to this question?
\(y=66-3x\)
Why is this the correct answer?
A linear rule has the form \(y=a+mx\), where \(a\) is the initial value and \(m\) is the change per step. Here, the initial value is 66 and the quantity decreases by 3 each step, so \(m=-3\). Therefore, the rule is \(y=66-3x\). The rule \(y=66+3x\) represents an increase of 3 per step, so it is not correct. Exam tip: the phrase “decreases by” indicates a negative slope.
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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