Which line cuts the (y)-axis at ( (0,9) ) and decreases (y) by (12) when (x) increases by (3)?
Answer and explanation
Correct answer: \(y=-4x+9\)
When \(x\) increases by 3 and \(y\) decreases by 12, the slope is \(m=\frac{-12}{3}=-4\). Since the line cuts the \(y\)-axis at \((0,9)\), its \(y\)-intercept is 9. Therefore, its equation is \(y=-4x+9\). Option A has a positive slope, but \(y\) is decreasing here. Exam tip: Use a negative sign for the slope whenever the dependent variable decreases.
Frequently asked questions
What is the correct answer to this question?
\(y=-4x+9\)
Why is this the correct answer?
When \(x\) increases by 3 and \(y\) decreases by 12, the slope is \(m=\frac{-12}{3}=-4\). Since the line cuts the \(y\)-axis at \((0,9)\), its \(y\)-intercept is 9. Therefore, its equation is \(y=-4x+9\). Option A has a positive slope, but \(y\) is decreasing here. Exam tip: Use a negative sign for the slope whenever the dependent variable decreases.
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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