In the line \(y=\frac{3}{2}x-4\), how much will (y) increase when (x) increases by (2)?
Answer and explanation
Correct answer: 3
The slope of \(y=\frac{3}{2}x-4\) is \(\frac{3}{2}\), so for every increase of 1 in \(x\), \(y\) increases by \(\frac{3}{2}\). Therefore, when \(x\) increases by 2, \(y\) increases by \(\frac{3}{2}\times2=3\). The constant \(-4\) is the y-intercept and does not affect the change. Exam tip: In \(y=mx+c\), use \(\Delta y=m\Delta x\) to find total change.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The slope of \(y=\frac{3}{2}x-4\) is \(\frac{3}{2}\), so for every increase of 1 in \(x\), \(y\) increases by \(\frac{3}{2}\). Therefore, when \(x\) increases by 2, \(y\) increases by \(\frac{3}{2}\times2=3\). The constant \(-4\) is the y-intercept and does not affect the change. Exam tip: In \(y=mx+c\), use \(\Delta y=m\Delta x\) to find total 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.
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