Which of these lines are parallel to y=2x+3? Which are perpendicular? Options: 1) y=5x-4, 2) y=-1/3x+3, 3) y=-1/2x-1, 4) y=2x-2/3

There are two ways of doing this question, one would be to sketch the graphs and see which are parallel to and which are perpendicular to the original line. Whilst this is valid, sketching lines isn’t always the easiest thing to do.The second way is to compare the lines with the general equation of a line, y=mx+c. In this equation, m is the slope of the line (or the gradient of the line) and c is where the line crosses the y axis (the y-intercept). For two lines to be parallel, they must have the same slope (i.e. the value of m will be the same for both lines). Therefore by looking at the different lines, we see that line 4 has the same slope as the original line and so is parallel to it. In order to check if two lines are perpendicular, we use the fact that when you multiply the slopes of two perpendicular lines together, you get -1 (sketch this to clarify what we mean). Checking this line by line, 2 times 5 is ten so line 1 is not perpendicular to the original line, 2 times -1/3 is -2/3 so line 2 is not perpendicular either, 2 times -1/2 is -1 so we can see that line 3 is perpendicular to the original line.