In the line \(y=\frac{5}{4}x-2\), how much will (y) increase when (x) increases by (12)?
Answer and explanation
Correct answer: 15
The slope of \(y=\frac{5}{4}x-2\) is \(\frac{5}{4}\). This means that for every increase of 4 units in \(x\), \(y\) increases by 5 units. Therefore, when \(x\) increases by 12 units, \(\Delta y=\frac{5}{4}\times 12=15\). The constant term \(-2\) gives the y-intercept and does not affect the change in \(y\). Exam tip: for \(y=mx+c\), use \(\Delta y=m\Delta x\).
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The slope of \(y=\frac{5}{4}x-2\) is \(\frac{5}{4}\). This means that for every increase of 4 units in \(x\), \(y\) increases by 5 units. Therefore, when \(x\) increases by 12 units, \(\Delta y=\frac{5}{4}\times 12=15\). The constant term \(-2\) gives the y-intercept and does not affect the change in \(y\). Exam tip: for \(y=mx+c\), use \(\Delta y=m\Delta x\).
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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