Chapter 3 Lesson 6

Objective:Objective: To relate slope to parallel lines.

2 4 6 8

2

4

6

8

-2-2

-4

-4

-6

-6

Remember:Remember: If two nonvertical lines are parallel, their slopes are equal.Example 1:

Checking for Parallel Lines

Are line l1 and l2 parallel? Explain.

(1,5)

(-2,-4)

(3,3)

(1,-4)

Slope of l1 )2(1)4(5

339

Slope of l2 13)4(3

27

Lines l1 and l2 are not parallel because their slopes are not equal.

Example 2:Example 2:Checking for Parallel LinesChecking 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 )4(321

71

Slope of l4 )4(802

61

122

Lines l3 and l4 are not parallel because their slopes are not equal.

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 0235

12

2

Slope of l2 03

)7(10

1

33

Lines l1 and l2 are parallel because their slopes are equal.

Example 3:Example 3:Checking for Parallel LinesChecking for Parallel Lines

Example 4:Determining Whether Lines are Parallel

Are the lines 4y-12x=20 and y=3x-1 parallel? Explain.Write 4y-12x=20 in slope-intercept form.

4y-12x=20

4y=12x+20

y=3x+5

Add 12x to each side.Add 12x to each side.

Divide each side by4.Divide each side by4.

The lines are parallel because they have the The lines are parallel because they have the same slope. same slope.

SlopSlopee

SlopSlopee

Example 5:Determining Whether Lines are Parallel

Are the lines y=-5x+4 and x=-5y+4 parallel? Explain.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.Subtract 4 from each side.

Divide each side by -5.Divide each side by -5.

The lines are not parallel because they have The lines are not parallel because they have different slopes. different slopes.

SlopSlopee

SlopSlopee

Example 6:Determining Whether Lines are Parallel

Are the lines y=(-1/2)x+5 and 2x+4y=9 parallel? Explain.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.Subtract 2x from each side.

Divide each side by 4.Divide each side by 4.

The lines are parallel because they have the The lines are parallel because they have the same slopes. same slopes.

SlopSlopee

SlopSlopee

Example 7:Writing Equations of Parallel Lines

Write an equation for the line parallel to y=-4x+3 that contains (1,-2).

SlopSlopee

Use point-slope form to write an equation for the Use point-slope form to write an equation for the new line.new line.

y-y1=mm(x-x1)

y-(-2)=-4-4(x-1)

y+2=-4(x-1)

xx11 yy11

y=mx+b

6x-3y=9

-3y=-6x+9

y=2x-3

Example 8:Writing Equations of Parallel Lines

Write an equation for the line parallel to 6x-3y=9 that contains (-5,-8).

SlopeSlope

Use point-slope form to Use point-slope form to write an equation for the write an equation for the new line.new line.

y-y1=mm(x-x1)

y-(-8)=22(x-(-5))

y+8=2(x+5)

xx11 yy11

Get 6x-3y=9 in slope-Get 6x-3y=9 in slope-intercept form.intercept form.

Assignment

Pg.161-163 #1-15;31-34;36-37; 39