In the line \(y=\frac{1}{4}x+6\), how much will (y) increase when (x) increases by (8)?
Answer and explanation
Correct answer: 2
In \(y=mx+c\), \(m\) is the slope, which gives the change in \(y\) for each 1-unit change in \(x\). Here, the slope is \(\frac{1}{4}\). Therefore, when \(x\) increases by 8, \(\Delta y=\frac{1}{4}\times 8=2\). The number 6 is the y-intercept, not the change in \(y\). Exam tip: multiply the slope by the change in \(x\) to find the change in \(y\).
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
In \(y=mx+c\), \(m\) is the slope, which gives the change in \(y\) for each 1-unit change in \(x\). Here, the slope is \(\frac{1}{4}\). Therefore, when \(x\) increases by 8, \(\Delta y=\frac{1}{4}\times 8=2\). The number 6 is the y-intercept, not the change in \(y\). Exam tip: multiply the slope by the change in \(x\) to find the change in \(y\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Slope and y-intercept.
