Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Eigenvalues and eigenvectors wikipedia , lookup

Quartic function wikipedia , lookup

Cubic function wikipedia , lookup

History of algebra wikipedia , lookup

Elementary algebra wikipedia , lookup

Signal-flow graph wikipedia , lookup

System of polynomial equations wikipedia , lookup

System of linear equations wikipedia , lookup

Equation wikipedia , lookup

Transcript
```October 12, 2016
Lesson 4.2
Graphing Linear Equations
To determine whether a given ordered pair is a
solution to an equation with two variables,
1. Replace the variables with the given values.
2. Verify that the equation is true.
Page 255 #11
Is (-5, 2) a solution to the equation y - 4x = 3?
Now try (-1, -1).
.
1
October 12, 2016
To find solutions to an equation with two variables,
1. Solve for one of the variables, usually y.
2. Replace the other variable, x, with values of your choice.
3. Simplify the resulting expression.
Find three solutions to the equation 4x - 3y = -12.
4x - 3y = -12
-3y = -4x - 12
y= 4 x+4
Solve the equation for y.
x
4
x+4
3
y
0
4
( )+4
3 0
4
3
4
( )+4
3 3
8
-3
4
( )+4
3 -3
0
3
•
10
•
•
-5
•
5
-10
.
2
October 12, 2016
To graph a linear equation,
1. Find at least three solutions to the equation.
2. Plot the point corresponding to the solutions.
3. Connect the points to form a straight line.
Graph y = 3x + 2
x
3x + 2
y
0
3( 0 ) + 2
2
1
3( 1 ) + 2
5
-1
3(-1 ) + 2
-1
•
•
•
•
•
•
•
Graph -7 = 3x + 2
3x+2=-7
•
3x=-9
x=-3
•
Now graph y = 2
.
3
October 12, 2016
Page 258 #65
A copy center charges \$15.00 for the first 300 copies plus
\$0.03 per copy after that. The equation c = 0.03n + 15 gives
the total cost for copy services, where n represents the
number of copies above 300.
a) What is the cost of 400 copies?
The cost of 400
copies is \$18.
b) How many copies were made if the cost is \$21?
The client was charged
for 500 copies.
c) Graph the equation.
•
30
24
18
•
•
12
6
100 200 300 400 500 600
.
4
October 12, 2016
6
4
2
-6
-4
2
-2
4
6
-2
-4
-6
5
```