In the line \(y=-\frac{5}{3}x+14\), how much should (x) increase to decrease (y) by (40)?
Answer and explanation
Correct answer: 24
The slope is \(-\frac{5}{3}\). Thus, for every increase of 3 units in \(x\), \(y\) decreases by 5 units. If the increase in \(x\) is \(\Delta x\), the decrease in \(y\) is \(\frac{5}{3}\Delta x\). Hence \(\frac{5}{3}\Delta x=40\), so \(\Delta x=40\times\frac{3}{5}=24\). Choosing 30 would decrease \(y\) by 50, not 40. Exam tip: a negative slope means that \(y\) decreases as \(x\) increases.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
The slope is \(-\frac{5}{3}\). Thus, for every increase of 3 units in \(x\), \(y\) decreases by 5 units. If the increase in \(x\) is \(\Delta x\), the decrease in \(y\) is \(\frac{5}{3}\Delta x\). Hence \(\frac{5}{3}\Delta x=40\), so \(\Delta x=40\times\frac{3}{5}=24\). Choosing 30 would decrease \(y\) by 50, not 40. Exam tip: a negative slope means that \(y\) decreases as \(x\) increases.
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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