8.1 SAT Math - Graphing/Coordinate Geometry

We covered some of the information regarding graphing in the Algebra sections of the SAT, in particular the basics of functions, but now we'll apply everything to the coordinate plane. 

Coordinate Plane

A coordinate plane is the official name for a graph with an x-axis and a y­-axis.
Points are laid out in ordered pairs, a set of parentheses in which the x value comes first, the y value second, like this:

Just remember to move side to side first, then up and down when you are plotting points.
-SAT Math Tip: If the answer choices are ordered pairs, make sure you look carefully.  The most common wrong answer choice has the ordered pair written (y, x), or has a negative in front of one of the numbers, or something equally minor.  Know which order the numbers are supposed to go in and don't be swayed by tricky answer choices.
To find the distance between two points, you can use the distance formula if you know it: .  Alternatively, you can draw a right triangle along the grid lines and use a² + b² = c² to solve for the distance requested:

12. The distance between points P and R is
(A) 1
(B) 3
(C) 4
(D) 2√5
(E) 4√5

Either use the distance formula, adding the squared differences between your x's and your y's, or draw a triangle and solve:

Midpoint

The midpoint of a line is found with the ordered pair: .
What is the midpoint of PR above? (-1, 0) 

Slope

The slope of a line is its steepness, just like a ski slope.  It is often referred to as , but the easiest way to remember slope and to solve for it is "y  minus y over x minus x" or .  It doesn't matter which ordered pair you use as y₂ and which as y₁, just make sure you keep it consistent – so whichever y goes first in your subtraction problem, make sure the corresponding x goes first.
Just like a ski slope, know which slopes are zero and which are undefined.  Can you ski a terrain that is flat?  Yes, you can, it just has no slope.  So a horizontal line has a slope of 0.  Can you ski a slope that goes straight up and down?  No, you'd fall to your death.  So a vertical line has an undefined slope – it's impossible.