In the line \(y=\frac{3}{4}x+2\), how much will (y) increase when (x) increases by (8)?
Answer and explanation
Correct answer: 6
The slope is \(\frac{3}{4}\), meaning that for every increase of 4 units in \(x\), \(y\) increases by 3 units. Hence, when \(x\) increases by 8, the change in \(y\) is \(\frac{3}{4}\times 8=6\). The constant 2 is the y-intercept, so it does not affect the increase. Exam tip: use \(\Delta y=m\Delta x\) to find the change in \(y\).
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The slope is \(\frac{3}{4}\), meaning that for every increase of 4 units in \(x\), \(y\) increases by 3 units. Hence, when \(x\) increases by 8, the change in \(y\) is \(\frac{3}{4}\times 8=6\). The constant 2 is the y-intercept, so it does not affect the increase. Exam tip: use \(\Delta y=m\Delta x\) 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.
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