The Rectangular Coordinate System Section 3.1 The Rectangular Coordinate System

The Rectangular Coordinate System A rectangular coordinate system consists of a horizontal number line and a vertical number line. x y 1 2 3 4 1 2 3 4 An ordered pair (x, y) represents a point on the coordinate system. y-axis x-axis The ordered pair (3, 4) means that x = 3 and y = 4. (3, 4)

Example Plot the points (4, 2), (3, 3), and (1, 0) on a rectangular coordinate system. x y 1 2 3 4 1 2 3 4 (4, 2) (1, 0) (3, 3)

Example Write the coordinates of each point plotted in the graph. y 1 2 3 4 1 2 3 4 A B C (4, 3) 3 units up a line parallel to the y-axis (2, 2) A = (4, 3) 4 units to the left on the x-axis B = (2, 2) (0, 3) C = (0, 3)

A linear equation in two variables is an equation that can be written in the form Ax + By = C where A, B, and C are real numbers but A and B are not both zero. A solution to a linear equation is an ordered pair that makes the equation a true mathematical statement.

Example Is (2, 1) is a solution to the equation 2x + y = 5. We replace values for x and y in the equation to see if we obtain a true statement. 2x + y = 5 2(2) + (1) = 5 4 + 1 = 5 5 = 5 The ordered pair (2, 1) is a solution to the equation.

Example a. Is (1, 5) is a solution to the equation x + y = 4. b. List two other ordered pairs that are solutions to the equation. We replace values for x and y in the equation to see if we obtain a true statement. x + y = 4 1 + 5 = 4 4 = 4 The ordered pair (1, 5) is a solution to the equation.

Example (cont) a. Is (1, 5) is a solution to the equation x + y = 4. b. List two other ordered pairs that are solutions to the equation. There are many ordered pairs that are solutions. So answers may vary. We can choose any two numbers whose sum is 4. Try (0, 4). x + y = 4 0 + 4 = 4 4 = 4 The ordered pair (0, 4) is a solution to the equation.

Example (cont) a. Is (1, 5) is a solution to the equation x + y = 4. b. List two other ordered pairs that are solutions to the equation. There are many ordered pairs that are solutions. So answers may vary. We can choose any two numbers whose sum is 4. Try (2, 2). x + y = 4 2 + 2 = 4 4 = 4 The ordered pair (2, 2) is a solution to the equation.

Example Find the missing coordinate to complete the following ordered-pair solution for the equation y = 6x + 5. a. (2, ?) b. (?, 7) y = 6x + 5 y = 6x + 5 y = 6(2) + 5 7 = 6x + 5 y = 12 + 5 12 = 6x y = 17 2 = x (2, 17) is a solution. (2, 7) is a solution.