The rectangular coordinate system, also called the Cartesian coordinate system or the x-y coordinate system is shown below.

Notice that the rectangular coordinate system consists of 4 quadrants, a horizontal axis, a vertical axis, and the origin. The horizontal axis is usually called the x-axis, and the vertical axis is usually called the y-axis. The origin is the point where the two axes cross. The coordinates of the origin are (0,0). This notation is called an ordered pair. The first coordinate (or abscissa) is known as the x-coordinate, while the second coordinate (or ordinate) is the y-coordinate. These tell how far and in what direction we move from the origin.

Example: Plot the point (-2, 3).

Notice that from the origin we go to the left 2 units then up 3 units. Then we plot the point.

A first degree equation (or linear equation) is an equation whose graph is a straight line.

The general form of a linear equation is Ax + By + C = 0 where A, B, and C are real constants, and A and B are not both zero.

When graphing an equation, we usually begin by creating a table of values. We do this by choosing a value for x or y, substituting that value in the equation and solving for the other variable. Two points we usually find are the x-intercept and the y-intercept. To find the x-intercept, we assign the value of y to be zero and solve for x. To find the y-intercept, we assign the value of x to be zero and solve for y. Although only two points are necessary to sketch the graph of a line, we usually choose three points so that we can check our work.

Example: Graph 2x - 3y = 6

If x = 0, then                                                                 If y = 0, then

2(0) - 3y = 6                                                                     2x - 3(0) = 6

0 - 3y = 6                                                                         2x - 0 = 6

-3y = 6                                                                             2x = 6

y = -2                                                                                x = 3

(0, -2)                                                                             (3, 0)

If x = -3, then

Connect the points with a straight line. We get

Example 2: Graph y = 2x - 4

If x = 0, then                                                           If y = 0, then

If x = -1, then

Example 3: Graph x = 3

This is the same as x + 0y = 3

Since the coefficient of y is 0, let's just choose values of y.

If y = 0, then                                         If y = 2, then

If y = -4, then

No matter what value y is x is always 3. When we graph this, we get:

(Connect the points.  The software I'm using won't let me draw a vertical line.)

Example 4: Graph y = -2.

This is equivalent to 0 x + y = -2.

Since the coefficient of x is 0, let's choose values for x.

If x = 0, then                                 If x = 2, then

(0, -2)                                                    

No matter what value x is y is always -2.

Stock Prices. An investor recorded the weekly stock prices for a share of a mutual fund. His incomplete records for 9 weeks are given in the line graph below. Use this graph to

a. Determine the price in week 3

b. Determine the price in week 5

c. Interpolate to approximate the price in week 6

d. Extrapolate to approximate the price in week 8

Connect these points to form a line graph. (I can't do that from this software.)

a. When x=3, y = 8. So the price in week 3 was $8.

b. When x = 5, y = 9. So the price in week 5 is $9.

c. From the graph it appears that the price is $8.50 when x = 6.

d. If this pattern continues for another week, it appears that the price in week 8 would be $7.50.