Download Section 4.2 - Mathmatuch

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.
Each input must be paired with only
ONE output
Not a function
Not a function
Function
x
0
2
4
4 8
x
1
1
2
3 5
x
1 2
3
4
5
y
4
3
2
1 0
y
4
3
2
1 0
y
3 3
6
8 10
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 line
The STANDARD or GENERAL
FORM of a linear equation is
represented as
Ax + By = C
where A, B, and C are real numbers
Linear Equations
An example of a linear equation in two variables is
-3x + 2y = 5
the solution of an equation in two variables, x
and y, is an ordered pair (x, y) that produces a
true statement when substituted into the
equation.
Which ordered pair is a solution of -3x + 2y = 5?
A. (3,4)
B. (1,-1)
C. (-1, 1)
D. (0,-1)
Graph an Equation
Graph the equation
y = -4 + 3x.
y  4  3x
x
-10
-1
-7
0
-4
2
-1
2
y = -4 + 3x
10
y
-2
1
y-axis
8
6
4
2
-12 -10 -8
-6 -4 -2
x-axis
0
(2,2)
2
4
-2(1,-1)
(0,-4)
-4
-6
(-1,-7)
-8
-10
(-2,-10)
6
8
10 12
Graph an Equation
Graph the equation
SOLUTION
STEP 1
Solve the equation for y.
y  2x  4
y  4  2x
y + 2x = 4.
STEP 2
STEP 3
Make a table by
choosing a few values
for x and then finding
values for y.
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
Graph the equation
SOLUTION
STEP 1
Solve the equation for y.
 2 x  y  3
y  2x  3
-2x + y = -3.
STEP 2
STEP 3
Make a table by
choosing a few values
for x and then finding
values for y.
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
Graph the equation
SOLUTION
STEP 1
Solve the equation for y.
0 x1y  2
y2
0x + 1y = 2.
STEP 2
STEP 3
Make a table by
choosing a few values
for x and then finding
values for y.
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
Graph the equation
SOLUTION
STEP 1
Solve the equation for x.
1 x  0 y  1
x  1
x = -1.
STEP 2
STEP 3
Make a table by
choosing a few values
for x and then finding
values for y.
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 FunctionThe equation Ax + By = C
represents a linear function as long as
B = 0.
Graph a Function
1
–
Graph the function y =
2 x + 4 with domain x ≥ 0.
Then identify the range of the function.
SOLUTION
STEP 1
Make a table.
x
0
2
4
6
8
y
4
3
2
1
0
STEP 2
Plot the points.
STEP 3
Connect the points with a ray
because the domain is restricted.
STEP 4
Identify 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
Graph the function y = – 3x + 1 with domain x ≤ 0.
Then identify the range of the function.
SOLUTION
STEP 1
Make a table.
x
0
–1
–2
–3
–4
y
1
4
7
10
13
STEP 2
Plot the points.
STEP 3
Connect the points with a ray
because the domain is restricted.
STEP 4
Identify 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.