If the line (y=-(p-1)x+16) decreases (y) by (35) when (x) increases by (5), what is (p)?
Answer and explanation
Correct answer: 8
The slope of the line is \(-(p-1)\). An increase of \(5\) in \(x\) and a decrease of \(35\) in \(y\) give \(\Delta y=-35\). Hence, the slope is \(\frac{-35}{5}=-7\). Therefore, \(-(p-1)=-7\), so \(p-1=7\) and \(p=8\). If \(p=7\), the slope would be \(-6\), not the required \(-7\). Exam tip: Write a decrease in \(y\) as a negative change before finding the slope.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The slope of the line is \(-(p-1)\). An increase of \(5\) in \(x\) and a decrease of \(35\) in \(y\) give \(\Delta y=-35\). Hence, the slope is \(\frac{-35}{5}=-7\). Therefore, \(-(p-1)=-7\), so \(p-1=7\) and \(p=8\). If \(p=7\), the slope would be \(-6\), not the required \(-7\). Exam tip: Write a decrease in \(y\) as a negative change before finding the slope.
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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