3.1 The Rectangular Coordinate System and Equations in Two Variables Learning Objectives: 1. Plot points in the rectangular coordinate system. 2. Determine if an ordered pair satisfies an equation. 3. Completing Ordered Pair Solutions. 4. Create a table of values that satisfy an equation. 1. Plot points in the rectangular coordinate system y
5
–5 –5
x
5
Example 1. Plot each ordered pair. State in which quadrant or on which axis each point lies. y a. (− 5, − 3) 5 ⎛ 3 5⎞
⎜− , ⎟ ⎝ 2 2⎠
b. x
5 –5 –5 2. Determine if an ordered pair satisfies an equation Definition: 1. Equation‐is an algebraic expression with “=” sign. 2. Solution of an Equation‐is the value of the variable that makes the equation true. Example 2. Determine whether each ordered pair is a solution of the equation 3x − y = 12 a. 1 (0, 12 ) b. (1, − 9) 3. Completing Ordered Pair Solutions Example 3. Complete each ordered pair so that it is a solution to the equation x + 2 y = 8 a. (0,
b. (
) ,−3) 4. Create a table of values that satisfy an equation Example 3. Complete the table for the following equation 1. y = −2 x x y (x, y ) − 3 0 10 2. 3x − 2 y = −6 x y (x, y ) − 3 −4 6 2