Linear Equations in Two Variables

Objective: Write a linear equation in two variables given different types of

information.

36

18

15

126

7;5 bm

xy

xy

01

Example 1

Example 1

Example 1

Example 1

Try This

• Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6)

Try This

• Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6)

1) Find the slope 21

2

21

46

Try This

• Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6)

1) Find the slope

2) Find the y-intercept

21

2

21

46

b

b

bmxy

8

)2)(2(4

Try This

• Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6)

1) Find the slope

2) Find the y-intercept

3) Write an equation

21

2

21

46

b

b

bmxy

8

)2)(2(4

82 xy

bmxy

Point-Slope Form

• You can use the point-slope form to write an equation of a line if you are given the slope and the coordinates of any point on the line or given two points.

Point-Slope Form

• You can use the point-slope form to write an equation of a line if you are given the slope and the coordinates of any point on the line or given two points.

Try This

• Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6)

Try This

• Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6)

1) Find the slope 21

2

21

46

Try This

• Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6)

1) Find the slope

2) Use point-slope form

21

2

21

46

82

424

)2(24

)( 11

xy

xy

xy

xxmyy

Try This

• Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6)

1) Find the slope

2) Use point-slope form

21

2

21

46

82

424

)2(24

)( 11

xy

xy

xy

xxmyy

82

226

)1(26

)( 11

xy

xy

xy

xxmyy

Example 2

Example 2

Example 2

Try This

• Write an equation in slope-intercept form for the line that has the slope of 3 and contains the point (2, -1).

Try This

• Write an equation in slope-intercept form for the line that has the slope of 3 and contains the point (2, -1).

• Begin with point-slope form)2(3)1(

)( 11

xy

xxmyy

Try This

• Write an equation in slope-intercept form for the line that has the slope of 3 and contains the point (2, -1).

• Begin with point-slope form

• Write an equation

)2(3)1(

)( 11

xy

xxmyy

73

631

xy

xy

Parallel Lines

• If two lines have the same slope, they are parallel.

• If two lines are parallel, they have the same slope.

• All vertical lines have an undefined slope and are parallel to one another.

• All horizontal lines have a slope of 0 and are parallel to one another.

Parallel Lines

Example 4

Example 4

Example 4

12

1

)1)(2(3

xy

b

b

bmxy

Example 4

12

1

)1)(2(3

xy

b

b

bmxy

Perpendicular Lines

• If a nonvertical line is perpendicular to another line, the slopes of the lines are negative reciprocals of one another.

• All vertical lines are perpendicular to all horizontal lines.

• All horizontal lines are perpendicular to all vertical lines.

Perpendicular Lines

Example 5

Example 5

Example 5

2

2

)4)((3

41

41

xy

b

b

bmxy

Example 5

Example 3

• Tim leaves his house and drives at a constant speed to go camping. On his way to the campgrounds, he stops to buy gas. Three hours after buying gas, Tim has traveled 220 miles from home, and 5 hours after buying gas he has traveled 350 miles from home. How far from home was Tim when he bought gas?

Example 3

• Write a linear equation to model Tim’s distance, y, in terms of time, x. Three hours after buying gas, Tim has traveled 220 miles, and 5 hours after buying gas, Tim has traveled 350 miles. The line contains the points (3, 220) and (5, 350).

Example 3

• Write a linear equation to model Tim’s distance, y, in terms of time, x. Three hours after buying gas, Tim has traveled 220 miles, and 5 hours after buying gas, Tim has traveled 350 miles. The line contains the points (3, 220) and (5, 350).

Example 3

• This equation models Tim’s distance from home with respect to time. Since x represents the number of hours he traveled after he bought gas, he bought gas when x = 0. Thus, he bought gas 25 miles from home.

325

413

23

)2(34

xy

xy

8

)10(2

53

53

xy

xy

325

413

23

)2(34

xy

xy

8

)10(2

53

53

xy

xy

62

)0(26

xy

xy

2

)3(2

34

34

xy

xy

8055

)4(55300

55

)465,7(&)300,4(

47300465

xy

xy

Homework

• Pages 26-27• 11-45 odd

• Please check your answers as you go and do all of the problems. You need practice to master this skill!