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8.3

The Rectangular Coordinate System and Paired Data. 8.3. The Rectangular Coordinate System. y -axis. 5. 4. quadrant II. quadrant I. 3. 2. origin. 1. (0,0). x -axis. - 5. - 4. -3. -2. -1. 1. 2. 3. 4. 5. -2. -3. - 4. quadrant III. quadrant IV. - 5. Plotting Points. y.

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8.3

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  1. The Rectangular Coordinate System and Paired Data 8.3

  2. The Rectangular Coordinate System y-axis 5 4 quadrant II quadrant I 3 2 origin 1 (0,0) x-axis -5 -4 -3 -2 -1 1 2 3 4 5 -2 -3 -4 quadrant III quadrant IV -5

  3. Plotting Points y 5 4 (4,3) 3 2 1 x -5 -4 -3 -2 -1 1 2 3 4 5 -2 -3 -4 -5

  4. Plotting Points In general, to plot the ordered pair (x,y), start at the origin. Next, (x,y) move x units left or right and then move y units up or down. right if x is positive, left if xis negative up if y is positive, down if y is negative

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

  6. Plotting Points y Plot the following: (2,1) (–3 ,4) (5,0) (0, –2) (1, –3) (–4, –5) 5 4 (–3,4) 3 2 (2,1) 1 (5,0) x -5 -4 -3 -2 -1 1 2 3 4 5 (0, –2) -2 -3 (1, –3) -4 (–4, –5) -5

  7. Helpful Hint Remember that each point in the rectangular coordinate system corresponds to exactly one orderedpair and that each ordered pair corresponds to exactly one point.

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

  9. ? 3(1) + 6 = 9 Completing Ordered Pair Solutions An equation in two variables, such as 3x + y = 9, has solutions consisting of two values, one for x and one for y. 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. 3x + y = 9 The solution x = 1 and y = 6 can be written as (1,6), an ordered pair of numbers. 9 = 9 True

  10. Solutions 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.

  11. Finding Solutions 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, ) ( , 4) Let x = 0 and solve for y. Let y = 4 and solve for x. 2x–y = 6 2x–y = 6 2(0) –y = 6 2x– 4= 6 0 –y = 6 2x = 10 y = – 6 x = 5 The ordered pair is (0, –6). The ordered pair is (5,4).

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