Objective: To relate slope to parallel lines.

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3.8 Slopes of Parallel and Perpendicular Lines

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Presentation transcript:

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

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)

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.

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.

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.

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.

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)

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

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