Rectangular Coordinate System Created by Laura Ralston

“A picture is worth a thousand words.” Graphs are widely used in the media. Newspapers and magazines, television, reports to stockholders, and newsletters all present information in the form of a graph. Graphs are used so widely because they show a lot of information in a form that makes it easy to understand

Ordered pairs Because we have two number lines, we need two numbers in order to find a solution. An ordered pair is a pair of numbers written within parentheses in which ORDER matters.

(x, y) The first number in the pair is called : – x-component – x-coordinate – independent variable – Abscissa – Input – It tells the number of units to move on the x- axis; that is, right or left. The second number in the pair is called: – y-component – y-coordinate – dependent variable – Ordinate – Output – It tells the number of units to move on the y- axis; that is up or down.

How to plot a point on the coordinate plane? To “plot” a point, start at the origin. Move “x” units right (positive) or left (negative) Move “y” units up (positive) or down (negative) feature=related

Equations with two variables Will have a solution with two numbers Often expressed as an ordered pair Remember a solution makes the equation TRUE To find a solution, we choose any number for one of the variables (usually “x”). Substitute into equation and solve for the other variable (“y”)

Equations continued….. Because every real number could be selected for one variable and would lead to a real number for the other variable, an equation with two variables has an infinite number of solutions The “graph” of an equation gives us a picture of the equation. That is, it corresponds to the set of points that satisfy the equation (make it true).

Graph of an Equation To graph an equation, we plot a number of ordered pairs (usually 3 - must plot 2) that are solutions to the equation. Q The points should appear to be in a straight line. Therefore, they are called ….

Linear Equations in 2 Variables Standard Form – Ax + By = C where A, B, and C are real numbers Variables on one side of equals sign in alphabetical order No fractions or decimals for A, B, or C “A” must be positive No exponents of variables

Two points useful for graphing are X-intercept – point where the line crosses the x-axis – at this point, y = 0 – Solve for x Y-intercept – point where the line crosses the y-axis – at this point, x = 0 – Solve for y.

Two special cases Horizontal Line – has no x-intercept – all ordered pairs have the same y-coordinate – y = b, where b is any number Vertical Line – has no y-intercept – all ordered pairs have the same x-coordinate – x = k, where k is any number