Of the following 4 equations, 3 of them represent parallel lines. Which is the odd one out?
- 2y - 3x = 4 2) -12x = 4(1 - 2y) 3) y - 5 = 3(x - 1)/2 4) 3(y - x) = 4 - y This question relies on the student's understanding of parallel lines as well as their ability to rearrange equations. The key piece of knowledge is that, for lines to be parallel, they must have the same gradient. The student then needs to be equipped to compare equations, either using the standard y = mx + c format, or through a more in depth understanding of relative attributes of an equation. I would provide the student with two solutions: 1a) 2y = 3x + 4 or 1b) y = 3x/2 + 2 2a) 8y = 12x + 4 or 2b) y = 3x/2 + 1/2 3a) 2y = 3x + 2 or 3b) y = 3x/2 + 1 4a) 4y = 3x + 4 or 4b) y = 3x/4 + 1 Based on the above rearranged equations, I would tutor my students to be able to answer the question more quickly using the results of a). This requires a greater understanding between the relative scalar of y compared to the relative scalar of x, but would enable more time in practice for other questions. The second method makes use of the standard y = mx + c equation of a line for a direct comparison between the values of x scalars. It is immediately obvious using this method that equation 4 is the odd one out, but this should also be visible in a) and is achievable upon a quick review of the initial equations; we can learn to see patterns in equations and show that in this case y = mx + c isn't necessarily required as the y scalars are very similar to begin with.
