In the xy-coordinate plane above, line 
contains the points (0,0) and (1,2). If line m (not shown) contains the point (0,0) and is perpendicular to , what is an equation of m?
There’s one very important rule you need to know here in order to answer this question correctly. Lines that are perpendicular to one another will always have slopes that are the negative reciprocals of each other. For example, if you have a line with a slope of 5, the line perpendicular to it will have a slope of -1/5. The other thing, which you will remember from Algebra class, is that the equation for a line is y=mx+b (m being the slope; b being the y-intercept). From the graph above, we can figure out the slope. One way to determine the slope of this line is to take the two points that are given to you (0,0 and 1,2) and plug them into this equation: [y(2)-y(1)]/[x(2)-x(1)], or in this case: (2-0)/(1-0)=2/1=2.
The slope is 2. The y-intercept, because the line passes through the origin (0,0) is zero. The equation for the line shown, then, is y=2x. The equation for the line perpendicular to it, as a result, is y=-1/2x. The answer is A.
Source: collegeboard.com
