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![Page 1: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/1.jpg)
Linear Equations in Two Variables
Objective: Write a linear equation in two variables given different types of
information.
![Page 2: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/2.jpg)
![Page 3: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/3.jpg)
36
18
15
126
7;5 bm
xy
xy
01
![Page 4: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/4.jpg)
Example 1
![Page 5: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/5.jpg)
Example 1
![Page 6: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/6.jpg)
Example 1
![Page 7: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/7.jpg)
Example 1
![Page 8: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/8.jpg)
Try This
• Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6)
![Page 9: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/9.jpg)
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
![Page 10: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/10.jpg)
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
![Page 11: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/11.jpg)
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
![Page 12: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/12.jpg)
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.
![Page 13: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/13.jpg)
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.
![Page 14: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/14.jpg)
Try This
• Write an equation in slope-intercept form for the line containing the points (2, 4) and (1, 6)
![Page 15: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/15.jpg)
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
![Page 16: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/16.jpg)
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
![Page 17: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/17.jpg)
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
![Page 18: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/18.jpg)
Example 2
![Page 19: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/19.jpg)
Example 2
![Page 20: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/20.jpg)
Example 2
![Page 21: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/21.jpg)
Try This
• Write an equation in slope-intercept form for the line that has the slope of 3 and contains the point (2, -1).
![Page 22: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/22.jpg)
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
![Page 23: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/23.jpg)
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
![Page 24: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/24.jpg)
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.
![Page 25: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/25.jpg)
Parallel Lines
![Page 26: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/26.jpg)
Example 4
![Page 27: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/27.jpg)
Example 4
![Page 28: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/28.jpg)
Example 4
12
1
)1)(2(3
xy
b
b
bmxy
![Page 29: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/29.jpg)
Example 4
12
1
)1)(2(3
xy
b
b
bmxy
![Page 30: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/30.jpg)
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.
![Page 31: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/31.jpg)
Perpendicular Lines
![Page 32: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/32.jpg)
Example 5
![Page 33: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/33.jpg)
Example 5
![Page 34: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/34.jpg)
Example 5
2
2
)4)((3
41
41
xy
b
b
bmxy
![Page 35: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/35.jpg)
Example 5
![Page 36: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/36.jpg)
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?
![Page 37: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/37.jpg)
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).
![Page 38: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/38.jpg)
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).
![Page 39: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/39.jpg)
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.
![Page 40: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/40.jpg)
![Page 41: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/41.jpg)
325
413
23
)2(34
xy
xy
8
)10(2
53
53
xy
xy
![Page 42: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/42.jpg)
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
![Page 43: Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.](https://reader033.fdocuments.in/reader033/viewer/2022061305/5513fae9550346dd488b460a/html5/thumbnails/43.jpg)
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!