warm-up 1) determine whether the point (0,3) is a solution to y = 5x + 3. 5 minutes 2) graph y = -2x...
DESCRIPTION
Linear Equations y = 3x + 76y = -2 9x – 15y = 7 Linear Equations Equations whose graphs are lines are linear equations. Here are some examples: Nonlinear Equations y = x 2 - 4x 2 + y 2 = 16 xy = 3TRANSCRIPT
Warm-Up1) Determine whether the point (0,3) is a solution to y = 5x + 3.
5 minutes
2) Graph y = -2x + 1
7.3.1 Linear Equations and Their 7.3.1 Linear Equations and Their GraphsGraphs
Objectives: •To graph linear equations in two variables
LinearEquations
y = 3x + 7 6y = -2 9x – 15y = 7
Linear EquationsEquations whose graphs are lines are linear equations.Here are some examples:
NonlinearEquations
y = x2 - 4 x2 + y2 = 16
xy = 3
2y x
Example 1Graph the equation 2x + 2y = 6.
2x + 2y = 6 x y
325
01-2
2x + 2y = 6
solve for y-2x -2x
2y = 6 – 2x2 2y = 3 - xy = 3 - (0) = 3y = 3 - (1) = 2y = 3 - (-2)= 5
Example 1Graph the equation 2x + 2y = 6.
2x + 2y = 6 x y
325
01-2
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
PracticeGraph these linear equations using three points.1) 3y – 12 = 9x 2) 4y + 8 = -16x
Example 2Graph the equation 3y – 6 = 9x.
3y – 6 = 9xx y
25-4
01-2
3y – 6 = 9x solve for y+6
+63y = 9x + 63 3y = 3x + 2y = 3(0) + 2
= 2y = 3(1) + 2
= 5y = 3(-2) + 2
= -4
Example 2Graph the equation 3y – 6 = 9x.
3y – 6 = 9xx y
25-4
01-2
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
PracticeGraph these linear equations using three points.1) 6x – 2y = -2 2) -10x – 2y = 8
Homeworkp.316 #1,3,7,11,15
*Use graph paper for the homework
Warm-Up6 minutes
1) Graph 4x – 3y = 12
* Get 2 sheets of graph paper and a ruler
7.3.2 Linear Equations and Their 7.3.2 Linear Equations and Their GraphsGraphs
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.
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8The line shown intercepts the x-axis at (2,0).
We say that the x-intercept is 2.
Graphing Using Intercepts
The y-intercept of a line is the y-coordinate of the point where the line intercepts the y-axis.
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
The line shown intercepts the y-axis at (0,-6).
We say that the y-intercept is -6.
Example 1Graph 4x – 3y = 12 using intercepts.
x y-40
4x – 3y = 12
*To find the y-intercept, let x = 0.
4(0) – 3y = 120 – 3y = 12
-3y = 12-3 -3
y = -4
Example 1Graph 4x – 3y = 12 using intercepts.
x y-40
03
4x – 3y = 12
*To find the x-intercept, let y = 0.
4x – 3(0) = 124x - 0 = 12
4x = 124 4x = 3
Example 1
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
Graph 4x – 3y = 12 using intercepts.
x y-40
03
Example 2Graph 2x + 5y = 10 using intercepts.
x y20
2x + 5y = 10
*To find the y-intercept, let x = 0.
2(0) + 5y = 100 + 5y = 10
5y = 105 5y = 2
Example 2Graph 2x + 5y = 10 using intercepts.
x y20
05
2x + 5y = 10
*To find the x-intercept, let y = 0.
2x + 5(0) = 102x + 0 = 10
2x = 102 2x = 5
Example 2
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
Graph 2x + 5y = 10 using intercepts.
x y20
05
PracticeGraph using intercepts.
1) 5x + 7y = 35 2) 8x + 2y = 24 3) 2y = 3x - 6
Homeworkp.316 #17,20,21,23,26,27
*Use graph paper for the homework
Warm-Up10 minutes
Graph these equations:1) -x + 2y = 42) 2x + 3y = 83) 2x – 1 = y4) 3x – 4y = -
12
7.3.3 Linear Equations and Their 7.3.3 Linear Equations and Their GraphsGraphs
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 =
126x + 7y = 23
Example 1
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
Graph y = -2.write the equation in standard form
Ax + By = C
(0)x + (1)y = -2
for any value of x
y = -2
Example 2
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
Graph x = 7.write the equation in standard form
Ax + By = C
(1)x + (0)y = 7
x = 7 for any value of y
PracticeGraph these equations.
1) x = 5 2) y = -4 3) x = 0
Homeworkp.316 #11,13,19,25,27,35,37,41
*Use graph paper for the homework