Transcript lesson 7.3 Linear Eq..

5 minutes
Warm-Up
1) Determine whether the point (0,3) is a
solution to y = 5x + 3.
2) Graph y = -2x + 1
7.3.1 Linear Equations and Their Graphs
Objectives:
•To graph linear equations in two variables
Linear Equations
Equations whose graphs are lines are linear equations.
Here are some examples:
Linear
Equations
y = 3x + 7
Nonlinear
Equations
x2
y=
-4
6y = -2
x2
+
y2
= 16
9x – 15y = 7
xy = 3
2
y
x
Example 1
Graph the equation 2x + 2y = 6.
2x + 2y = 6
solve for y
-2x
-2x
2y = 6 – 2x
2
2
y=3-x
y = 3 - (0) = 3
y = 3 - (1) = 2
y = 3 - (-2) = 5
2x + 2y = 6
x
0
1
-2
y
3
2
5
Example 1
Graph the equation 2x + 2y = 6.
8
2x + 2y = 6
6
4
2
-8 -6
-4
-2
-2
-4
-6
-8
2
4
6
8
x
0
1
-2
y
3
2
5
Practice
Graph these linear equations using three
points.
1) 3y – 12 = 9x
2) 4y + 8 = -16x
Example 2
Graph the equation 3y – 6 = 9x.
3y – 6 = 9x
solve for y
+6
+6
3y = 9x + 6
3
3
y = 3x + 2
y = 3(0) + 2 = 2
y = 3(1) + 2 = 5
y = 3(-2) + 2 = -4
3y – 6 = 9x
x
0
1
-2
y
2
5
-4
Example 2
Graph the equation 3y – 6 = 9x.
8
3y – 6 = 9x
6
4
2
-8 -6
-4
-2
-2
-4
-6
-8
2
4
6
8
x
0
1
-2
y
2
5
-4
Practice
Graph these linear equations using three
points.
1) 6x – 2y = -2
2) -10x – 2y = 8
Homework
p.316 #1,3,7,11,15
*Use graph paper for the homework
6 minutes
Warm-Up
1) Graph 4x – 3y = 12
* Get 2 sheets of graph paper and a ruler
7.3.2 Linear Equations and Their Graphs
Objectives:
•To graph linear equations using intercepts
Graphing Using Intercepts
The x-intercept of a line is the x-coordinate of the
point where the line intercepts the x-axis.
The line shown intercepts the
x-axis at (2,0).
8
6
4
We say that the x-intercept is 2.
2
-8 -6
-4
-2
-2
-4
-6
-8
2
4
6
8
Graphing Using Intercepts
The y-intercept of a line is the y-coordinate of the
point where the line intercepts the y-axis.
The line shown intercepts the
y-axis at (0,-6).
8
6
We say that the y-intercept is -6.
4
2
-8 -6
-4
-2
-2
-4
-6
-8
2
4
6
8
Example 1
Graph 4x – 3y = 12 using intercepts.
*To find the y-intercept, let x = 0.
4x – 3y = 12
4(0) – 3y = 12
0 – 3y = 12
-3y = 12
-3 -3
y = -4
x
0
y
-4
Example 1
Graph 4x – 3y = 12 using intercepts.
*To find the x-intercept, let y = 0.
4x – 3y = 12
4x – 3(0) = 12
4x - 0 = 12
4x = 12
4
4
x=3
x
0
3
y
-4
0
Example 1
Graph 4x – 3y = 12 using intercepts.
8
6
4
2
-8 -6
-4
-2
-2
-4
-6
-8
2
4
6
8
x
0
3
y
-4
0
Example 2
Graph 2x + 5y = 10 using intercepts.
*To find the y-intercept, let x = 0.
2x + 5y = 10
2(0) + 5y = 10
0 + 5y = 10
5y = 10
5
5
y=2
x
0
y
2
Example 2
Graph 2x + 5y = 10 using intercepts.
*To find the x-intercept, let y = 0.
2x + 5y = 10
2x + 5(0) = 10
2x + 0 = 10
2x = 10
2
2
x=5
x
0
5
y
2
0
Example 2
Graph 2x + 5y = 10 using intercepts.
8
6
4
2
-8 -6
-4
-2
-2
-4
-6
-8
2
4
6
8
x
0
5
y
2
0
Practice
Graph using intercepts.
1) 5x + 7y = 35
2) 8x + 2y = 24
3) 2y = 3x - 6
Homework
p.316 #17,20,21,23,26,27
*Use graph paper for the homework
10 minutes
Warm-Up
Graph these equations:
1) -x + 2y = 4
2) 2x + 3y = 8
3) 2x – 1 = y
4) 3x – 4y = -12
7.3.3 Linear Equations and Their Graphs
Objectives:
•To graph linear equations that graph as horizontal and
vertical lines
Graphing Horizontal and Vertical Lines
The standard form of a linear equation in two
variables is Ax + By = C, where A,B, and C are
constants and A and B are not both 0.
3x + 4y = 12
6x + 7y = 23
Example 1
Graph y = -2.
Ax + By = C
write the equation
in standard form
(0)x + (1)y = -2
8
6
4
for any
value of x
y = -2
2
-8 -6
-4
-2
-2
-4
-6
-8
2
4
6
8
Example 2
Graph x = 7.
Ax + By = C
write the equation
in standard form
(1)x + (0)y = 7
8
6
4
x=7
for any
value of y
2
-8 -6
-4
-2
-2
-4
-6
-8
2
4
6
8
Practice
Graph these equations.
1) x = 5
2) y = -4
3) x = 0
Homework
p.316 #11,13,19,25,27,35,37,41
*Use graph paper for the homework