In the line \(y=\frac{7}{3}x-5\), how much should (x) increase to increase (y) by (21)?
Answer and explanation
Correct answer: 9
The slope is \(\frac{7}{3}\), meaning that an increase of 3 units in \(x\) increases \(y\) by 7 units. For \(\Delta y=21\), we use \(\frac{7}{3}\Delta x=21\). Hence, \(\Delta x=21\times\frac{3}{7}=9\). If \(x\) increased by 7, then \(y\) would increase by only \(\frac{49}{3}\), not 21. 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?
9
Why is this the correct answer?
The slope is \(\frac{7}{3}\), meaning that an increase of 3 units in \(x\) increases \(y\) by 7 units. For \(\Delta y=21\), we use \(\frac{7}{3}\Delta x=21\). Hence, \(\Delta x=21\times\frac{3}{7}=9\). If \(x\) increased by 7, then \(y\) would increase by only \(\frac{49}{3}\), not 21. 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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