The first step in x/y graphing is identifying the x and y axes on a standard coordinate plain. A coordinate plain looks like a big plus or right angle with tick marks and numbers at evenly spaced intervals going up and down it, and arrowheads at the ends of the lines. The point where the two perpendicular lines meet is called the origin. The horizontal line is the x-axis, where x coordinates are graphed, and the vertical line is the y-axis, where y coordinates are graphed.
Every point on a graph is represented by two numbers in parentheses separated by a comma: (x,y). The first number is on the x axis and the second number on the y. To graph a point, count the number of units over on the x axis, then the number up or down on the y. All coordinates are in relationship to the origin at (0,0). For example, to graph (5,-3), count five units to the right of the origin, then move 3 units down and mark the point. A coordinate with 0 is drawn on the axis; for example (0,4) is drawn at 4 on the y-axis.
Sometimes you need to use a formula to find coordinates. In this case, plug a coordinate, usually an x value, into the formula and what you get is the y coordinate. So given the formula y = 3x + 2, pick numbers for x, say, 0, 1, -2 and 3, and plug them into the formula to get 2, 5, -4 and 11, respectively, giving you the coordinates (0,2), (1,5), (-2,-4), (3,11). Graph these points and draw a line connecting them. Pick points that are close together and include some negatives to see both sides of the graph.
Sometimes finding the coordinates is not as simple as plugging inputs into a formula because of all the variables, coefficients and exponents involved in the equation. Sometimes there are special tricks or formulas, like factoring or using the quadratic formula for x^2, or quadratic, functions. For most complicated equations, such as y^3 = 1/5x^4 - 14x + 6, your simplest bet to find the graph is to plug it into a graphing calculator.