In the line \(y=-\frac{4}{5}x+12\), how much will (y) decrease when (x) increases by (15)?
Answer and explanation
Correct answer: (12)
In a linear equation written as y=mx+c, the coefficient m tells how much y changes when x changes by one unit. Here the slope is -4/5, so y moves downward as x increases. The negative sign indicates decrease, while the magnitude 4/5 gives the size of the change per unit increase in x.
When x increases by 15, the change in y is \\(\Delta y=\left(-\frac{4}{5}\right)(15)=-12\\). Thus y becomes 12 units smaller, so the requested decrease is 12, not -12. The constant 12 is the y-intercept and does not affect this change. Therefore option C is correct.
Frequently asked questions
What is the correct answer to this question?
(12)
Why is this the correct answer?
In a linear equation written as y=mx+c, the coefficient m tells how much y changes when x changes by one unit. Here the slope is -4/5, so y moves downward as x increases. The negative sign indicates decrease, while the magnitude 4/5 gives the size of the change per unit increase in x.
When x increases by 15, the change in y is \\(\Delta y=\left(-\frac{4}{5}\right)(15)=-12\\). Thus y becomes 12 units smaller, so the requested decrease is 12, not -12. The constant 12 is the y-intercept and does not affect this change. Therefore option C is correct.
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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