1. Algebra 1 Graphing Equations With a Table of Values

2. Objective Students will graph equations using a table. Students will graph equations using a table. Students will graph horizontal and vertical lines Students will graph horizontal and vertical lines Students will graph a variety of equations, including linear, quadratic, and exponential. Students will graph a variety of equations, including linear, quadratic, and exponential.

3. Cartesian Plane Basics Vocabulary: Cartesian coordinate system: splitting the plane into four quadrants and numbering: Y axis X Axis Origin (0,0) Quadrant I Quadrant IV Quadrant III Quadrant II

4. Cartesian Plane Basics Vocabulary: Horizontal ACROSS Vertical up/down Plot: (-3, 4) Plot: (3, 4) Plot: (-3, -4) Plot (3, -4) Y axis X Axis Quadrant I Quadrant IV Quadrant III Quadrant II

5. Cartesian Plane Basics Vocabulary: Independent variables: choose any thing legal,graph vertically on y axis. Dependent variables: maintain the relationship by following the rule, graphed horizontally on x axis Think of something numerical that depends on another value. For instance: Soda costs $1 If I buy 3 cans it is $3. Y = 3x is linear equation. HW I will give you the equation! Make a T-chart and plot.

6. Cartesian Plane Basics Vocabulary: Graph: visual representation of a variable dependent on another. Y = cost X = number of cans. Y = 3x is linear equation. Make a T-chart and plot. Choose x, x y FIND y from equation.

7. To Graph with a Table of Values 1. Choose at least 5 values (both positive and negative) for x to plug into a table. 2. Plug those values one at a time into the equation for x, and solve for y. 3. Plot those (x,y) ordered pairs on the coordinate plane. 4. Follow the pattern of the graph to extend the line through the coordinate plane.

8. Example #1 y = 2x – 1 1. Choose values for x 2. Substitute the value of x into the equation 3. Simplify to determine the value of y 4. Write as an ordered pair

9. (x, y) (0, - 1) (1, 1) (2, 3) x y (0, -1) (1,1) (2,3) y = 2x – 1

10. Comments How do you choose the value of x? How do you choose the value of x? You can use any number for the value of x…however, you can make your life easy by choosing -1, 0, and 1, because you can do mental math and they are easy to graph. You can use any number for the value of x…however, you can make your life easy by choosing -1, 0, and 1, because you can do mental math and they are easy to graph. You choose a minimum of 5 numbers because you need enough to see what the line will do. You choose a minimum of 5 numbers because you need enough to see what the line will do.

11. Cartesian Plane Basics 1.) y = 3x + 5 T chart choose x find y. x y 0 5 -1 2 1 8 2.) Plot & Connect points 3.) Extend line and locate x-int & y-int

12. Cartesian Plane Basics 1.) y = 3x + 5 T chart choose x find y. x y 0 5 -1 2 1 8 2.) Plot & Connect points 3.) Extend line, locate x-int & y-int: x–int =( -1.7, 0) y- int = (0, 5)

13. Example #2 – Horizontal Line Graph the equation y=2 Graph the equation y=2 In this instance there is no x-value. All the y-values = 2 In this instance there is no x-value. All the y-values = 2

14. Example #2 (Continued) x yy=2 y=2

15. Example #3 – Vertical Line Graph the equation x = -3 Graph the equation x = -3 In this instance there is no y-value. All the x-values = -3 In this instance there is no y-value. All the x-values = -3 xy(x,y) -3(-3,-1) -30(-3,0) -31(-3,1)

16. You try Graph by plotting using a table of values: Use -2, -1, 0, 1, and 2 for your x values 1. Y = -3x + 1