Algebra 1Algebra 1

Graphing Equations Graphing Equations

With a Table of ValuesWith a Table of Values

ObjectiveObjective

Students will graph equations using a Students will graph equations using a table.table.

Students will graph horizontal and Students will graph horizontal and vertical linesvertical lines

Students will graph a variety of Students will graph a variety of equations, including linear, equations, including linear, quadratic, and exponential.quadratic, and exponential.

Cartesian Plane BasicsVocabulary: Cartesian coordinate system: splitting the plane into four quadrants and numbering:

Y axis

X Axis

Origin (0,0)

Quadrant I

Quadrant IVQuadrant III

Quadrant II

Cartesian Plane BasicsVocabulary: Horizontal ACROSS Vertical up/down

Plot: (-3, 4)

Plot: (3, 4)

Plot: (-3, -4)

Plot (3, -4)

Y axis

X Axis

Quadrant I

Quadrant IVQuadrant III

Quadrant II

Cartesian Plane BasicsVocabulary: 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 $1If 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.

Cartesian Plane BasicsVocabulary: Graph: visual representation of a variable dependent on another.Y = costX = number of cans. Y = 3x is linear equation.Make a T-chart and plot.Choose x, x y

FIND y from equation.

To Graph with a Table of To Graph with a Table of ValuesValues

1.1. Choose at least 5 values (both positive Choose at least 5 values (both positive and negative) for x to plug into a table.and negative) for x to plug into a table.

2.2. Plug those values one at a time into Plug those values one at a time into the equation for x, and solve for y.the equation for x, and solve for y.

3.3. Plot those (x,y) ordered pairs on the Plot those (x,y) ordered pairs on the coordinate plane.coordinate plane.

4.4. Follow the pattern of the graph to Follow the pattern of the graph to extend the line through the coordinate extend the line through the coordinate plane. plane.

Example #1Example #1y = 2x – 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

(x, y)(x, y)

(0, - 1)(0, - 1)

(1, 1)(1, 1)

(2, 3)(2, 3)

x

y

(0, -1)

(1,1)

(2,3)

y =

2x

– 1

y =

2x

– 1

CommentsComments 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 You can use any number for the value of x…however, you can make your life easy by x…however, you can make your life easy by choosing -1, 0, and 1, because you can do choosing -1, 0, and 1, because you can do mental math and they are easy to graph.mental math and they are easy to graph.

You choose a minimum of 5 numbers You choose a minimum of 5 numbers because you need enough to see what the because you need enough to see what the line will do. line will do.

Cartesian Plane Basics

1.) y = 3x + 5T 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

Cartesian Plane Basics

1.) y = 3x + 5T 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)

Example #2 – Horizontal Example #2 – Horizontal LineLine

Graph the equation y=2Graph the equation y=2

In this instance there is no x-value. In this instance there is no x-value. All the y-values = 2All the y-values = 2

Example #2 (Continued)Example #2 (Continued)

x

y

y=2y=2

y=2y=2

Example #3 – Vertical LineExample #3 – Vertical Line

Graph the equation x = -3Graph the equation x = -3

In this instance there is no y-value. In this instance there is no y-value. All the x-values = -3All the x-values = -3

x y (x,y)

-3 -1 (-3,-1)

-3 0 (-3,0)

-3 1 (-3,1)

You tryYou try

Graph by plotting using a table of Graph by plotting using a table of values:values:

Use -2, -1, 0, 1, and 2 for your x valuesUse -2, -1, 0, 1, and 2 for your x values

1.1.Y = -3x + 1Y = -3x + 1