In the line \(y=\frac{4}{3}x-6\), how much should (x) increase to increase (y) by (24)?
Answer and explanation
Correct answer: 18
The slope is \(\frac{4}{3}\), meaning that for every increase of 3 units in \(x\), \(y\) increases by 4 units. Thus, \(\Delta y=\frac{4}{3}\Delta x\). Putting \(\Delta y=24\), we get \(24=\frac{4}{3}\Delta x\), so \(\Delta x=24\times\frac{3}{4}=18\). If \(x\) increased by 24, then \(y\) would increase by 32, not 24. Exam tip: In change-based questions, the constant term \(-6\) does not affect the change; use only the slope.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The slope is \(\frac{4}{3}\), meaning that for every increase of 3 units in \(x\), \(y\) increases by 4 units. Thus, \(\Delta y=\frac{4}{3}\Delta x\). Putting \(\Delta y=24\), we get \(24=\frac{4}{3}\Delta x\), so \(\Delta x=24\times\frac{3}{4}=18\). If \(x\) increased by 24, then \(y\) would increase by 32, not 24. Exam tip: In change-based questions, the constant term \(-6\) does not affect the change; use only the slope.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Slope and y-intercept.
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