-3 1 2 3 4 5 -1 -2 -4 -5 -6 Y-axis A Quadrant 2 Quadrant I (4,2) 2 up 4 right 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 X-axis B C Quadrant 4 Quadrant 3 Each point is called an ordered pair. ( x, y)

-3 1 2 3 4 5 -1 -2 -4 -5 -6 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 Plot each ordered pair A= ( 2, -6) C = ( -5, 0) B = (0, 4) D = ( - 4, - 5) E = ( 4, 3/2)

-3 1 2 3 4 5 -1 -2 -4 -5 -6 All points on the x axis have y values equal to 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 All points on the y axis have x values equal to 0.

-3 1 2 3 4 5 -1 -2 -4 -5 -6 All points have y = 3 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 All points have y = -4 Conclusion: All points on Horizontal lines have the same y value!!!!

-3 1 2 3 4 5 -1 -2 -4 -5 -6 All points have x = -4 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 All points have x = 2 Conclusion: All points on a vertical line have the same x value!!!!

1) What is the balance in the account after 3 months? $6000 2) What is the balance in the account after 8 months? $3000

Equations in Two Variables 2x + 3y = -4 y = x² + 9 y = x³ - 1

To solve an equation with one variable, such as x + 3 = 7 means to find the value for x that makes the equation true. The solution is x = 4. Question :What does it mean to solve an equation, like - 2x + y = 1 that has two variables? Answer: To find all ordered pairs from the cartesian coordinate system that makes the equation true.

Let’s look at -2x + y = 1 Is ( 0, 2) a solution? -2(0) + ( 2) = 1 0 + 2 = 1 False Try ( 2, 5) -2(2) + ( 5) = 1 -4 + 5 = 1 True Try ( -1, -1 ) -2( -1) + ( -1) = 1 2 + (-1) = 1 True

How do you find solutions to an Equation in Two Variables? You simply plug in x values and solve the equation for y. Let’s return to the equation -2x + y = 1 If I plug in x = 3, then I can find the corresponding y value -2( 3) + y = 1 So ( 3, 7) is a solution to the equation. - 6 + y = 1 y = 7

x y (x,y) Find more solutions for - 2x + y = 1 by filling in the chart -2 -3 (-2,-3) 1 3 (1,3) 5 2 (2,5) 1 (0, 1) -1 -1 (-1,-1)

-3 1 2 3 4 5 -1 -2 -4 -5 -6 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 All the points on this line represent solutions to the equation -2x + y = 1