In the line \(y=-\frac{5}{3}x+7\), how much will (y) change when (x) increases by (3)?
Answer and explanation
Correct answer: Decreases by 5
The slope of the line is \(-\frac{5}{3}\). This means that for every increase of 3 units in \(x\), \(y\) decreases by 5 units. Thus, \(\Delta y=-\frac{5}{3}\times 3=-5\), so \(y\) decreases by 5. In option B, 3 is the denominator of the slope, while 7 is only the y-intercept and does not affect the change. 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?
Decreases by 5
Why is this the correct answer?
The slope of the line is \(-\frac{5}{3}\). This means that for every increase of 3 units in \(x\), \(y\) decreases by 5 units. Thus, \(\Delta y=-\frac{5}{3}\times 3=-5\), so \(y\) decreases by 5. In option B, 3 is the denominator of the slope, while 7 is only the y-intercept and does not affect the change. 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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