IMC 2010 Q15
15. Bill is trying to sketch the graph of \(y = 2x + 6\) but in drawing the axes he has placed the \(x\)-axis up the page and the \(y\)-axis across the page. Which of these five graphs is a correct sketch of \(y = 2x + 6\) when the axes are placed in this way?
Intermediate Mathematical Challenge 2010, Question 15. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E
The line \(y = 2x + 6\) intersects the \(y\)-axis when \(x = 0\) and \(y = 6\). It intersects the \(x\)-axis when \(x = -3\) and \(y = 0\). So E is the correct line.
(Alternatively: \(y = 2x + 6\) may be rearranged to give \(x = \tfrac{1}{2}y - 3\). So the required line looks the same as the line \(y = \tfrac{1}{2}x - 3\) when the axes are drawn in the traditional way.)
Solution © UK Mathematics Trust, from the IMC 2010 solutions.