In the line \(y=-\frac{5}{6}x+20\), what is the total change in (y) when (x) increases from (0) to (18)?
Answer and explanation
Correct answer: Decreases by \(15\)
The slope is \(-\frac{5}{6}\), so for every increase of 6 units in \(x\), \(y\) decreases by 5 units. Here, \(\Delta x=18\), so \(\Delta y=-\frac{5}{6}\times18=-15\). Therefore, \(y\) decreases by \(15\) units in total. The value \(20\) is the y-intercept, not the change in \(y\). Exam tip: find total change by multiplying the slope by \(\Delta x\).
Frequently asked questions
What is the correct answer to this question?
Decreases by \(15\)
Why is this the correct answer?
The slope is \(-\frac{5}{6}\), so for every increase of 6 units in \(x\), \(y\) decreases by 5 units. Here, \(\Delta x=18\), so \(\Delta y=-\frac{5}{6}\times18=-15\). Therefore, \(y\) decreases by \(15\) units in total. The value \(20\) is the y-intercept, not the change in \(y\). Exam tip: find total change by multiplying the slope by \(\Delta x\).
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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