Which line cuts the (y)-axis at ( (0,-6) ) and increases (y) by (10) when (x) increases by (2)?
Answer and explanation
Correct answer: \(y=5x-6\)
An increase of \(10\) in \(y\) for an increase of \(2\) in \(x\) gives the slope \(m=\frac{10}{2}=5\). Since the line crosses the \(y\)-axis at \((0,-6)\), its \(y\)-intercept is \(b=-6\). Using \(y=mx+b\), the equation is \(y=5x-6\). The option \(y=10x-6\) has the correct intercept but an incorrect slope of \(10\). Exam tip: find the slope from the rate of change first, then identify the intercept by putting \(x=0\).
Frequently asked questions
What is the correct answer to this question?
\(y=5x-6\)
Why is this the correct answer?
An increase of \(10\) in \(y\) for an increase of \(2\) in \(x\) gives the slope \(m=\frac{10}{2}=5\). Since the line crosses the \(y\)-axis at \((0,-6)\), its \(y\)-intercept is \(b=-6\). Using \(y=mx+b\), the equation is \(y=5x-6\). The option \(y=10x-6\) has the correct intercept but an incorrect slope of \(10\). Exam tip: find the slope from the rate of change first, then identify the intercept by putting \(x=0\).
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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