Which line cuts the (y)-axis at ( (0,12) ) and decreases (y) by (20) when (x) increases by (4)?
Answer and explanation
Correct answer: \(y=-5x+12\)
When \(x\) increases by \(4\) and \(y\) decreases by \(20\), the slope is \(m=\frac{-20}{4}=-5\). Since the line meets the \(y\)-axis at \((0,12)\), its \(y\)-intercept is \(12\). Therefore, the equation is \(y=-5x+12\). Although \(y=-20x+12\) has the correct intercept, its slope is \(-20\), not \(-5\). Exam tip: Use a negative sign for the change in \(y\) when the quantity decreases.
Frequently asked questions
What is the correct answer to this question?
\(y=-5x+12\)
Why is this the correct answer?
When \(x\) increases by \(4\) and \(y\) decreases by \(20\), the slope is \(m=\frac{-20}{4}=-5\). Since the line meets the \(y\)-axis at \((0,12)\), its \(y\)-intercept is \(12\). Therefore, the equation is \(y=-5x+12\). Although \(y=-20x+12\) has the correct intercept, its slope is \(-20\), not \(-5\). Exam tip: Use a negative sign for the change in \(y\) when the quantity 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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