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

2. 2468 2 4 6 8 -2 -4 -6 Remember: Remember: If two nonvertical lines are parallel, their slopes are equal. Example 1: Checking for Parallel Lines Are line l 1 and l 2 parallel? Explain. (1,5) (-2,-4) (3,3) (1,-4) Slope of l 1 Slope of l 2 Lines l 1 and l 2 are not parallel because their slopes are not equal.

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

4. 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. Divide each side by4. The lines are parallel because they have the same slope. Slope Slope

5. 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. Divide each side by -5. The lines are not parallel because they have different slopes. Slope Slope

6. 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. Divide each side by 4. The lines are parallel because they have the same slopes. Slope Slope

7. Example 7: Writing Equations of Parallel Lines Write an equation for the line parallel to y=-4x+3 that contains (1,-2). Slope Use point-slope form to write an equation for the new line. m y-y 1 =m(x-x 1 ) -4 y-(-2)=-4(x-1) y+2=-4(x-1) x1x1x1x1 y1y1y1y1

8. 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). Slope Use point-slope form to write an equation for the new line. m y-y 1 =m(x-x 1 ) 2 y-(-8)=2(x-(-5)) y+8=2(x+5) x1x1x1x1 y1y1y1y1 Get 6x-3y=9 in slope-intercept form.

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