If the line (y=(k-3)x+2) increases (y) by (48) when (x) increases by (6), what is (k)?
Answer and explanation
Correct answer: \(11\)
The slope of the line is \(k-3\). Since \(y\) increases by \(48\) when \(x\) increases by \(6\), the slope is \(\frac{48}{6}=8\). Thus, \(k-3=8\), so \(k=11\). If \(k=10\), the slope would be only \(7\), giving a rise of \(42\) for a run of \(6\). Exam tip: in \(y=mx+c\), \(m\) is the slope.
Frequently asked questions
What is the correct answer to this question?
\(11\)
Why is this the correct answer?
The slope of the line is \(k-3\). Since \(y\) increases by \(48\) when \(x\) increases by \(6\), the slope is \(\frac{48}{6}=8\). Thus, \(k-3=8\), so \(k=11\). If \(k=10\), the slope would be only \(7\), giving a rise of \(42\) for a run of \(6\). Exam tip: in \(y=mx+c\), \(m\) is 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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