1. Objective: To relate slope to parallel lines.
Chapter 3 Lesson 6
Objective: To relate slope to parallel lines.

2. Checking for Parallel Lines
Remember: If two nonvertical lines are parallel, their slopes are equal.
Example 1:
Checking for Parallel Lines
Are line l1 and l2 parallel? Explain. 2 4 6 8 -2 -4 -6
Slope of l1
(1,5)
Slope of l2
(3,3)
Lines l1 and l2 are not parallel because their slopes are not equal.
(-2,-4)
(1,-4)

3. Example 2: Checking for Parallel Lines
Line l3 contains A(-4,2) and B(3,1). Line l4 contains C(-4,0) and D(8,-2). Are l3 and l4 parallel? Explain.
Slope of l3
Slope of l4
Lines l3 and l4 are not parallel because their slopes are not equal.
Example 3: Checking for Parallel Lines
Line l1 contains P(0,3) and Q(-2,5). Line l2 contains R(0,-7) and S(3,-10). Are l1 and l2 parallel? Explain.
Slope of l1
Slope of l2
Lines l1 and l2 are parallel because their slopes are equal.

4. Example 4: Determining Whether Lines are Parallel
Are the lines 4y-12x=20 and y=3x-1 parallel? Explain.
Slope
Write 4y-12x=20 in slope-intercept form.
4y-12x=20
4y=12x+20
y=3x+5
Add 12x to each side.
Divide each side by4.
Slope
The lines are parallel because they have the same slope.

5. Example 5: Determining Whether Lines are Parallel
Are the lines y=-5x+4 and x=-5y+4 parallel? Explain.
Slope
Write x=-5y+4 in slope-intercept form.
x=-5y+4
x-4=-5y
(-1/5)x+5/4=y
Subtract 4 from each side.
Divide each side by -5.
Slope
The lines are not parallel because they have different slopes.

6. Example 6: Determining Whether Lines are Parallel
Are the lines y=(-1/2)x+5 and 2x+4y=9 parallel? Explain.
Slope
Write 2x+4y=9 in slope-intercept form.
2x+4y=9
4y=-2x+9
y=(-1/2)x+(9/4)
Subtract 2x from each side.
Divide each side by 4.
Slope
The lines are parallel because they have the same slopes.

7. Example 7: Writing Equations of Parallel Lines
Write an equation for the line parallel to y=-4x+3 that contains (1,-2).
Slope x1 y1
Use point-slope form to write an equation for the new line.
y-y1=m(x-x1)
y-(-2)=-4(x-1)
y+2=-4(x-1)

8. Example 8: Writing Equations of Parallel Lines
Write an equation for the line parallel to 6x-3y=9 that contains (-5,-8). x1 y1
Get 6x-3y=9 in slope-intercept form.
Use point-slope form to write an equation for the new line.
y=mx+b
6x-3y=9
-3y=-6x+9
y=2x-3
y-y1=m(x-x1)
y-(-8)=2(x-(-5))
y+8=2(x+5)
Slope

9. Homework Pg
#1-15;31-34;36-37