In the line \(y=\frac{5}{2}x-1\), how much should (x) increase to increase (y) by (20)?
Answer and explanation
Correct answer: 8
The slope is \(\frac{5}{2}\), meaning that an increase of 2 units in \(x\) increases \(y\) by 5 units. Hence, \(\Delta y=\frac{5}{2}\Delta x\). Putting \(\Delta y=20\), we get \(20=\frac{5}{2}\Delta x\), so \(\Delta x=20\times\frac{2}{5}=8\). If \(x\) increased by 10, \(y\) would increase by 25, not 20. Exam tip: For a line \(y=mx+c\), use \(\Delta y=m\Delta x\) in change-based questions.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The slope is \(\frac{5}{2}\), meaning that an increase of 2 units in \(x\) increases \(y\) by 5 units. Hence, \(\Delta y=\frac{5}{2}\Delta x\). Putting \(\Delta y=20\), we get \(20=\frac{5}{2}\Delta x\), so \(\Delta x=20\times\frac{2}{5}=8\). If \(x\) increased by 10, \(y\) would increase by 25, not 20. Exam tip: For a line \(y=mx+c\), use \(\Delta y=m\Delta x\) in change-based questions.
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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