Algebra 1 CH 5.5 Write Equations of Parallel and Perpendicular Lines ...
Algebra 1 CH 5.5 Write Equations of Parallel and Perpendicular Lines.notebook January 14, 2015 Write Equations of Parallel and Perpendicular Lines
Write Equations of Parallel and Perpendicular Lines
Objective: Writing equations of parallel and perpendicular lines
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Parallel Lines: If two lines have the same slope then the lines are parallel.
What does it mean when two lines are parallel lines?
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Determine whether the given two lines are parallel. Line 1: 4x +y =8 Line 2: 6x +2y =12
y=2x +2
y= 2x1
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Line 1: 4x +y =8
Line 2: 6x +2y =12 Standard Form:
Recall: Since these lines are in standard form we can use the equation to find the slope.
In order to find if these two lines are parallel we need to find their slope.
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Determine whether the given two lines are parallel.
Line 1:
Line 2: Are these two lines parallel? Yes
Line 1:
Changing the yintercept will give us parallel lines:
Line 2:
Are these two lines parallel?
NO because they have different slopes
Dec 111:30 AM
Dec 111:30 AM
1
Algebra 1 CH 5.5 Write Equations of Parallel and Perpendicular Lines.notebook January 14, 2015 Write Equations of Parallel and Perpendicular Lines
Write Equations of Parallel and Perpendicular Lines
Write an equation of the line that passes through the given point (2,3) and is parallel to the line 4x+2y = 2
First we need to find the slope of the line.
We can either find the slope by using:
OR
Rewriting the equation in slopeintercept form
m = 2
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Write an equation of the line that passes through the given point (2,3) and is parallel to the line 4x+2y = 2
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
The equation of a line that is parallel to 4x+2y=2 and contains the point (2,3) is: y = 2x 1
Then plug in the given coordinates into the slopeintercept equation and solve for b
3 = (2)(2) + b
3 = 4 + b
b = 1
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Perpendicular lines two lines that intersect to form a right angle.
Write an equation of the line 2x + 5y = 10 that passes through the point (4,1) and is perpendicular to the given line
What is the slope of the given line?
The slope of the lines will be negative reciprocals of each other.
What is the negative reciprocal?
Example:
The negative reciprocal of 8 is
Dec 111:30 AM
Dec 111:30 AM
2
Algebra 1 CH 5.5 Write Equations of Parallel and Perpendicular Lines.notebook January 14, 2015 Write Equations of Parallel and Perpendicular Lines
Write Equations of Parallel and Perpendicular Lines
Write an equation of the line 2x + 5y = 10 that passes through the point (4,1) and is perpendicular to the given line.
The equation of the line perpendicular to 2x + 5y = 10 through the point (4,1) is :
Then we plug in the values of x and y into the equation and solve for b.
Dec 111:30 AM
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Write Equations of Parallel and Perpendicular Lines
The graph represents a ball bouncing off a wall. a
Determine which lines,if any, are parallel or perpendicular.
Line a:
Line b:
b
Write an equation that models line a and line b.
Line c:
What should we do first?
Line a :
Find the slope of the lines Line a: 5
Line b:
Line c:
Line b:
Do the lines form a right angle?
Line a and line b are perpendicular Dec 111:30 AM
Yes! Line a and line b are perpendicular because the slopes are negative reciprocals of each other.
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Objective: Writing equations of parallel and perpendicular lines
What we know now:
Parallel lines have the same slope
and
Perpendicular lines have negative reciprocal slopes
Dec 111:30 AM
3
Write Equations of Parallel and Perpendicular Lines
Objective: Writing equations of parallel and perpendicular lines
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Parallel Lines: If two lines have the same slope then the lines are parallel.
What does it mean when two lines are parallel lines?
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Determine whether the given two lines are parallel. Line 1: 4x +y =8 Line 2: 6x +2y =12
y=2x +2
y= 2x1
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Line 1: 4x +y =8
Line 2: 6x +2y =12 Standard Form:
Recall: Since these lines are in standard form we can use the equation to find the slope.
In order to find if these two lines are parallel we need to find their slope.
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Determine whether the given two lines are parallel.
Line 1:
Line 2: Are these two lines parallel? Yes
Line 1:
Changing the yintercept will give us parallel lines:
Line 2:
Are these two lines parallel?
NO because they have different slopes
Dec 111:30 AM
Dec 111:30 AM
1
Algebra 1 CH 5.5 Write Equations of Parallel and Perpendicular Lines.notebook January 14, 2015 Write Equations of Parallel and Perpendicular Lines
Write Equations of Parallel and Perpendicular Lines
Write an equation of the line that passes through the given point (2,3) and is parallel to the line 4x+2y = 2
First we need to find the slope of the line.
We can either find the slope by using:
OR
Rewriting the equation in slopeintercept form
m = 2
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Write an equation of the line that passes through the given point (2,3) and is parallel to the line 4x+2y = 2
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
The equation of a line that is parallel to 4x+2y=2 and contains the point (2,3) is: y = 2x 1
Then plug in the given coordinates into the slopeintercept equation and solve for b
3 = (2)(2) + b
3 = 4 + b
b = 1
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Perpendicular lines two lines that intersect to form a right angle.
Write an equation of the line 2x + 5y = 10 that passes through the point (4,1) and is perpendicular to the given line
What is the slope of the given line?
The slope of the lines will be negative reciprocals of each other.
What is the negative reciprocal?
Example:
The negative reciprocal of 8 is
Dec 111:30 AM
Dec 111:30 AM
2
Algebra 1 CH 5.5 Write Equations of Parallel and Perpendicular Lines.notebook January 14, 2015 Write Equations of Parallel and Perpendicular Lines
Write Equations of Parallel and Perpendicular Lines
Write an equation of the line 2x + 5y = 10 that passes through the point (4,1) and is perpendicular to the given line.
The equation of the line perpendicular to 2x + 5y = 10 through the point (4,1) is :
Then we plug in the values of x and y into the equation and solve for b.
Dec 111:30 AM
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Write Equations of Parallel and Perpendicular Lines
The graph represents a ball bouncing off a wall. a
Determine which lines,if any, are parallel or perpendicular.
Line a:
Line b:
b
Write an equation that models line a and line b.
Line c:
What should we do first?
Line a :
Find the slope of the lines Line a: 5
Line b:
Line c:
Line b:
Do the lines form a right angle?
Line a and line b are perpendicular Dec 111:30 AM
Yes! Line a and line b are perpendicular because the slopes are negative reciprocals of each other.
Dec 111:30 AM
Write Equations of Parallel and Perpendicular Lines
Objective: Writing equations of parallel and perpendicular lines
What we know now:
Parallel lines have the same slope
and
Perpendicular lines have negative reciprocal slopes
Dec 111:30 AM
3
