In the line \(y=-\frac{3}{2}x+10\), how much should (x) increase to decrease (y) by (18)?
Answer and explanation
Correct answer: 12
The slope is \(-\frac{3}{2}\). Thus, for every increase of 2 units in \(x\), \(y\) decreases by 3 units. If the increase in \(x\) is \(\Delta x\), the decrease in \(y\) is \(\frac{3}{2}\Delta x\). Hence, \(\frac{3}{2}\Delta x=18\), so \(\Delta x=12\). If 13 were chosen, the decrease would be \(\frac{3}{2}\times13=19.5\), not 18. Exam tip: With a negative slope, increasing \(x\) decreases \(y\).
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The slope is \(-\frac{3}{2}\). Thus, for every increase of 2 units in \(x\), \(y\) decreases by 3 units. If the increase in \(x\) is \(\Delta x\), the decrease in \(y\) is \(\frac{3}{2}\Delta x\). Hence, \(\frac{3}{2}\Delta x=18\), so \(\Delta x=12\). If 13 were chosen, the decrease would be \(\frac{3}{2}\times13=19.5\), not 18. Exam tip: With a negative slope, increasing \(x\) decreases \(y\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Slope and y-intercept.
