If (y=(r-4)x+(r+6)) passes through the origin, what will be its slope?
Answer and explanation
Correct answer: \(-10\)
The line is \(y=(r-4)x+(r+6)\). Since it passes through the origin \((0,0)\), substituting \(x=0\) and \(y=0\) gives \(r+6=0\). Hence, \(r=-6\). Therefore, the slope is \(r-4=-6-4=-10\). Note that \(-6\) is the value of the parameter \(r\), not the slope. Exam tip: in \(y=mx+c\), \(m\) is the slope and \(c\) is the y-intercept.
Frequently asked questions
What is the correct answer to this question?
\(-10\)
Why is this the correct answer?
The line is \(y=(r-4)x+(r+6)\). Since it passes through the origin \((0,0)\), substituting \(x=0\) and \(y=0\) gives \(r+6=0\). Hence, \(r=-6\). Therefore, the slope is \(r-4=-6-4=-10\). Note that \(-6\) is the value of the parameter \(r\), not the slope. Exam tip: in \(y=mx+c\), \(m\) is the slope and \(c\) is the y-intercept.
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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