In the line \(y=\frac{3}{4}x-8\), what is the total change in (y) when (x) increases from (4) to (16)?
Answer and explanation
Correct answer: Increases by 9
The slope is \(\frac{3}{4}\), so for every increase of 4 units in \(x\), \(y\) increases by 3 units. Here, \(\Delta x=16-4=12\). Therefore, \(\Delta y=\frac{3}{4}\times12=9\). Hence, \(y\) increases by 9. Note that 12 is the change in \(x\), not in \(y\). Exam tip: use \(\Delta y=m\Delta x\) for total change; the constant term \(-8\) does not affect the change.
Frequently asked questions
What is the correct answer to this question?
Increases by 9
Why is this the correct answer?
The slope is \(\frac{3}{4}\), so for every increase of 4 units in \(x\), \(y\) increases by 3 units. Here, \(\Delta x=16-4=12\). Therefore, \(\Delta y=\frac{3}{4}\times12=9\). Hence, \(y\) increases by 9. Note that 12 is the change in \(x\), not in \(y\). Exam tip: use \(\Delta y=m\Delta x\) for total change; the constant term \(-8\) does not affect the change.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Slope and y-intercept.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
