Do Now 10/26/10

In your notebook, explain how you know a function is a function. Then answer if the following three tables are functions or not.

x 0 2 4 4 8

y 4 3 2 1 0

x 1 1 2 3 5

y 4 3 2 1 0

x 1 2 3 4 5

y 3 3 6 8 10

Each input must be paired with Each input must be paired with only only ONEONE output output

Not a functionNot a function FunctionFunctionNot a functionNot a function

Objective

graph 7 linear equations and linear functions in a coordinate plane

Section 4.2 “Graph Linear Equations”

Linear Equation-an equation whose graph is a linean equation whose graph is a line

The The STANDARD or GENERAL STANDARD or GENERAL FORMFORM of a linear equation is of a linear equation is

represented asrepresented as

AAx x ++ BBy y = C= Cwhere A, B, and C are real where A, B, and C are real

numbersnumbers

Linear EquationsLinear Equations

An example of a linear equation in two variables is An example of a linear equation in two variables is

-3x + 2y = 5-3x + 2y = 5the solution of an equation in two variables, the solution of an equation in two variables, x x andand y y, is an ordered pair , is an ordered pair (x, y)(x, y) that produces a that produces a true statement when substituted into the true statement when substituted into the equation. equation.

Which ordered pair is a solution of -3x + 2y = 5?Which ordered pair is a solution of -3x + 2y = 5?

A. (3,4) B. (1,-1) C. (-1, 1) D. (0,-1)A. (3,4) B. (1,-1) C. (-1, 1) D. (0,-1)

22

44

66

88

1010

00 22 44 66 88 1010 1212

y-axisy-axis

x-axisx-axis

((-2-2,,-10-10))

-12-12 -10-10 -8-8 -6-6 -4-4 -2-2

-10-10

-8-8

-6-6

-4-4

-2-2

Graph an EquationGraph the equation Graph the equation y = -4 + 3xy = -4 + 3x..

xx yy

xy 34

-2-2 -10-10

-1-1 -7-7

((-1-1,,-7-7))

00 -4-4

((00,,-4-4))11 -1-1 ((11,,-1-1))

22 22

((22,,22))

y = -4 + 3xy = -4 + 3x

Graph an Equation

42 xy

xy 24

Solve the equation for y.

STEPSTEP 11

SOLUTION

Graph the equation Graph the equation y + 2x = 4 y + 2x = 4..

STEPSTEP 22

Make a table by choosing a few values for x and then finding values for y.

STEPSTEP 33

Plot the points. Notice the points appear on a line. Connect the points drawing a line through them.

x -2 -1 0 1 2

y 8 6 4 2 0

Graph an Equation

3yx2

32 xy

Solve the equation for y.

STEPSTEP 11

SOLUTION

Graph the equation Graph the equation -2x + y = -3-2x + y = -3..

STEPSTEP 22

Make a table by choosing a few values for x and then finding values for y.

STEPSTEP 33

Plot the points. Notice the points appear on a line. Connect the points drawing a line through them.

x -2 -1 0 1 2

y -7 -5 -3 -1 1

Graph an Equation

2y1x0

2y

Solve the equation for y.

STEPSTEP 11

SOLUTION

Graph the equation Graph the equation 0x + 1y = 20x + 1y = 2..

STEPSTEP 22

Make a table by choosing a few values for x and then finding values for y.

STEPSTEP 33

Plot the points. Notice the points appear on a line. Connect the points drawing a line through them.

x -2 -1 0 1 2

y 2 2 2 2 2

Graph an Equation

1y0x1

1x

Solve the equation for x.

STEPSTEP 11

SOLUTION

Graph the equation Graph the equation x = -1x = -1..

STEPSTEP 22

Make a table by choosing a few values for x and then finding values for y.

STEPSTEP 33

Plot the points. Notice the points appear on a line. Connect the points drawing a line through them.

x -1 -1 -1 -1 -1

y -2 -1 0 1 2

Linear Function-The equation The equation AAx x ++ BBy y = C = C represents a linear function as represents a linear function as

long as long as B = 0.B = 0.

Graph a Function

SOLUTION

1122Graph the functionGraph the function yy == – – xx + 4+ 4 with domainwith domain x x ≥≥ 0.0.

Then identify the range of the functionThen identify the range of the function..

STEP 1Make a table.

x 0 2 4 6 8

y 4 3 2 1 0

STEP 2

STEP 3Connect the points with a ray because the domain is restricted.

Plot the points.

STEP 4Identify the range. From the graph, you can see that all points have a y-coordinate of 4 or less, so the range of the function is y ≤ 4.

Graph a Function

SOLUTION

STEP 1Make a table.

STEP 2

STEP 3Connect the points with a ray because the domain is restricted.

Plot the points.

STEP 4Identify the range. From the graph, you can see that all points have a y-coordinate of 1 or more, so the range of the function is y ≥ 1.

Graph the function y = – 3x + 1 with domain x ≤ 0. Then identify the range of the function.

x 0 – 1 – 2 – 3 – 4

y 1 4 7 10 13