In the line y = -(5/6)x + 11, how much will y decrease when x increases by 12?
Answer and explanation
Correct answer: 10
The governing concept is that the slope measures the change in y per unit change in x. In y = -(5/6)x + 11, the slope is m = -5/6. For an increase of Δx = 12, calculate the vertical change using Δy = mΔx: Δy = (-5/6)(12) = -10. The negative sign means that y decreases, and the amount of the decrease is the positive magnitude 10. Hence option C is correct. The constant 11 does not affect the change because it is added to every value of y and only determines the y-intercept. Options A and B result from mishandling the fraction, while option D confuses the horizontal change with the vertical change.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The governing concept is that the slope measures the change in y per unit change in x. In y = -(5/6)x + 11, the slope is m = -5/6. For an increase of Δx = 12, calculate the vertical change using Δy = mΔx: Δy = (-5/6)(12) = -10. The negative sign means that y decreases, and the amount of the decrease is the positive magnitude 10. Hence option C is correct. The constant 11 does not affect the change because it is added to every value of y and only determines the y-intercept. Options A and B result from mishandling the fraction, while option D confuses the horizontal change with the vertical 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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