Linear Equations in Two Variables Objective: Write a linear equation in two variables given different types of information.
Mar 26, 2015
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!