Transcript Lesson 3.6 Writing Equations of Lines

Warm Up
Identify the slope and y-intercept
1. -3x + 5y = 9
Graph the equation.
2. -2x + 4y = 8
3. 2x + 7y = 7
Answers:
3
9
1. y  x 
5
5
3
9
m  b  (0, )
5
5
1
2. y  x  2
2
Warm Up Answers Continued
2
3. y   x  1
7
Lesson 7.1A
Writing equations for lines
that are parallel or
coinciding to a given line.
Parallel Lines
• Parallel lines have the same slope
(m) and different y intercept (b).
Example 1:
m = 3/1 , b = 6
y = 3x + 6
m = 3/1 , b = -7
y = 3x - 7
What are the slopes of these lines?
What are the slopes for any lines parallel
to each other?
The same
•
Coinciding Lines
Coinciding lines have the same
(m)
slope and same y-intercept (b).
Example 2:
y = 3x + 6
6y = 18x +36
m = 3/1 , b = 6
m = 3/1 , b = 6
Find m and b for each line.
What do you notice about m and b?
m and b are the same on both lines.
Parallel, Coinciding or Neither?
1) y = 4x + 2
y = 4x - 2
m = 4/1, m=4/1
parallel
3) y = 5x + 2
2y = 10x + 4
2) y = 2x + 7
y = 3x + 7
m = 2, m= 3
neither
4) y = 3x -6
y = 5 + 3x
m = 5, m = 5
m = 3/1, m= 3/1
coinciding
parallel
Example 3: Write the equation of the
line that is parallel to y = 2x + 3 and
goes through the point (-1, 5)
• Step 1: Find the slope.
m=2
• Step 2. Substitute given
x, y into the equation.
5 = 2 ( -1) + b
• Step 3: Solve for b.
5 = -2 + b
7=b
• Step 4: Substitute m and
b into the equation.
Y = ___x + ___.
Y = 2x + 7
Example 4: Write the equation of the
line that is parallel to 5y = -4x + 15
and goes through the point (-10, 2)
•
Step 1: Find the slope.
m = -4/5
•
Step 2. Substitute given x,y into
the equation.
2 = -4/5 ( -10) + b
•
Step 3: Solve for b.
2=8+b
-6 = b
•
Step 4: Substitute m and b into
the equation.
Y = ___x + ___.
Y = -4/5x -6
You try:
• Write an equation that is parallel to
y = 4x-5 thru the point (3,6).
y = 4x - 6
• Write an equation that is parallel to
3x - y = 7 thru the point (0,3)
y = 3x + 3
Summary:
• What is the difference between parallel
lines and coinciding lines when writing
equations?
Homework Worksheet 7.1A