The Rectangular Coordinate System and Paired Data Section 8.3

origin quadrant I quadrant II quadrant III quadrant IV The Rectangular Coordinate System x-axis y-axis (0,0) 2

Plotting Points x y 2 (4,3) 3

In general, to plot the ordered pair (x,y), start at the origin. Next, right if x is positive, left if x is negative up if y is positive, down if y is negative move units left or right and then move units up or down. move x units left or right and then move y units up or down. (x,y)(x,y) 4 Martin-Gay, Prealgebra, 5ed

Since the first number, or x-coordinate, x-coordinate, of an ordered pair is associated with the x-axis, x-axis, it tells how many units to move left or right. Similarly, the second number, or or y-coordinate, tells how many units to move up or down. Helpful Hint 5 Martin-Gay, Prealgebra, 5ed

Plot,,,,, and. Plot (2,1), (- 3,4), (5,0), (0,- 2), (1,- 3), and (- 4,- 5) x y (2,1) (- 3,4) (5,0) (- 4,- 5) (0,- 2) (1,- 3) 6

Remember that each point point in the rectangular coordinate system corresponds to exactly one ordered ordered pair and that each ordered pair pair corresponds to exactly one point. Helpful Hint 7 Martin-Gay, Prealgebra, 5ed

If an ordered pair has a y-coordinate y-coordinate of 0, its graph lies on the x-axis. x-axis. If an ordered pair has an x-coordinate x-coordinate of 0, its graph lies on the y-axis. Order Order is the key word in ordered pair. The first value always corresponds to the x-value x-value and the second value always corresponds to the y-value. Helpful Hint 8 Martin-Gay, Prealgebra, 5ed

Completing Ordered Pair Solutions An equation in two variables, such as 3x 3x + y = 9, has solutions consisting of two values, one for x and one for y.y. x 1y 6 For example, x = 1 and y = 6 is a solution of 3x + y = 9, because, if x is replaced with 1 and y is replaced with 6, we get a true statement. xy 3x + y = 9 1 3(1) + 6 = 9 ? 9 = 9 True The solution x = 1 and y = 6 can be written as (1,6), an ordered pair of numbers. 9 Martin-Gay, Prealgebra, 5ed

true statement In general, an ordered pair is a solution of an equation in two variables if replacing the variables by the values of the ordered pair results in a true statement. 10 Martin-Gay, Prealgebra, 5ed

If the x-value of an ordered pair is known, then the y-value can be determined, and vice-versa. Complete each ordered pair so that it is a solution to the equation 2x - y = 6. (0, ) x = 0 Let x = 0 and solve for y. x2x x2x - y = 6 0 2(0) - y = y = 6 y = - 6 (, 4) y = 4 Let y = 4 and solve for x. 2x 2x - y = 6 2x 2x - 4 = 6 2x 2x = 10 x = 5 The ordered pair is (0,- 6).The ordered pair is (5,4). 11

Helpful Hint two variablesmore than one solution Equations in two variables can have more than one solution. Have you noticed? 12 Martin-Gay, Prealgebra, 5ed