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