The diagram shows four sketch graphs, A, B, C and D.
(a) Write down the letter of the graph that could show
(i) $y$ is directly proportional to $x$ [1]
(ii) $y$ is directly proportional to $x^2$ [1]
(iii) $y$ is inversely proportional to $x$ [1]
(b) Graph C is a straight line. Give a reason why graph C does not show $y$ directly proportional to $x$. [1]
- (a)(i) DB1
- (a)(ii) AB1
- (a)(iii) BB1
- (b) the line does not pass through the origin (accept: when $x = 0$, $y$ is not $0$; or it has a $y$-intercept; ignore 'not proportional' without reason)C1
- Answer: (a)(i) D (ii) A (iii) B (b) It does not pass through the origin.
- Examiner tip: A straight line only shows direct proportion if it goes through $(0, 0)$: check the intercept, not just the shape.