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Chapter 3 Lesson 6

Chapter 3 Lesson 6. Objective: To relate slope to parallel lines. 8. 6. 4. 2. -4. 2. 4. 6. 8. -6. -2. -2. -4. -6. 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.

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Chapter 3 Lesson 6

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

  2. 8 6 4 2 -4 2 4 6 8 -6 -2 -2 -4 -6 Remember: If two nonvertical lines are parallel, their slopes are equal. Example 1: Checking for Parallel Lines Are line l1 and l2 parallel? Explain. 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. Assignment Pg.161-163 #1-15;31-34;36-37; 39

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