1. Algebra 4.1 Graphing Equations of Lines

2. The Coordinate Plane x axis HORIZONTAL y axis VERTICAL Origin (0,0)

3. Quadrant II ( -, + ) Quadrant I ( +, + ) Quadrant III ( -, - ) Quadrant IV ( +, - )

4. Let’s check out plotting points http://www.shodor.org/interactivate/ activities/GeneralCoordinates/

5. Equations in two variables, x and y Consider the equation: y = 2x + 3 There are an infinite number of combinations of x and y that will make this equation true. Each of these combinations is called an ordered pair (x,y) Each of these ordered pairs is called a solution of the equation.

6. y = 2x + 3 What is a solution? How do you find the ordered pair? Choose a value for x and plug it in. Let’s choose x = 2 y = 2(2) + 3 y = 7 So, when x = 2, y = 7 One solution to this equation is the ordered pair ( 2, 7 )

7. What are some other solutions to this equation? What is y when x = 0 ? So the ordered pair (0,3) is one solution What is y when x = 1 ? So the ordered pair (1,5) is another solution What is y when x = -1 ? So the ordered pair (-1,1) is another solution y = 2x + 3 y = 3 y = 5 y = 1

8. x y y = 2x + 3 2 7 15 03 1. (2,7). (0,3). (1,5). (-1,1) x y

9. x y y = 2x + 3 2 7 15 03 1. (2,7). (0,3). (1,5). (-1,1) x y This is the graph of the equation y = 2x + 3

10. Graphing the Equation for a Line using an X/Y Table STEPS 1.Rewrite the equation in slope- intercept form ( y = mx + b) 2.Set up an x/y table and choose three values for x (negative, 0, positive) 3.Plug in each x to compute each y 4.Plot the three ordered pairs (x,y) 5.Connect the points as a straight line

11. Graph: y = x - 1 Hint: Choose values for x that are multiples of 3. This will make it easier to compute y. x y -3 0 6 3. (0,-1). (6,3). (-3,-3) x y

12. Graph: y = x - 1 Hint: Choose values for x that are multiples of 3. This will make it easier to compute y. x y -3 0 6 3. (0,-1). (6,3). (-3,-3) x y The 3 points connect in a line

13. Every single point on a line represents a combination of (x, y) that makes the equation true. A line is a picture of all the solutions to an equation. Key Concepts

14. Graphing W/S Tuesday Math Lab or Lunch A-Ariel, Kelly C. 2-Nhigel, Matt, Alyssa 3-Evan, Grace, Brett, Adam, Seth, Andrew Homework