Parallel and Perpendicular Lines Ms. Houghton Geometry Honors Unit 3 Parallel and Perpendicular Lines Ms. Houghton Geometry Honors

Vocabulary Skew Lines Collinear Transversal Parallel Lines Two lines that will never intersect The slopes are the same Perpendicular Lines Two lines that intersect to form 4 right angles The slopes are negative reciprocals Negative reciprocal means the sign changes and the fraction flips. Skew Lines 2 lines that will not intersect only because they are on 2 different planes Collinear Points on the same line Transversal Any line that intersects 2 parallel lines

Parallel Lines What do we know about parallel lines? Are the following lines parallel? Y=3x+5 Y=3x-2 Y=(-5/3)x+2 Y=(5/3)x-3 Y=4x-5 3y-5x=5 Y+5=4x 4y+8x-3=0 Y-3x=5 Y=3 4y+12x=8 X=4

Create a line parallel to… Create an equation for a line parallel to y = 4x - 5 that goes through the point (4,2) What is the basic form of the equation? y = mx+b What does the slope have to be? Slope must = 4 What do we know? y =4x + b Do we know b(y-intercept)? Do we know y? x? y = 2 and x = 4

Create a line parallel to… 2=4(4)+B 2=16+B -14 = B Now rewrite the equation Y=MX+B Y=4X-14 Ask yourself is Y=4X-14 parallel to Y=4X+5

Your turn Find the equation of a line that parallel to y = -3x-4 that goes through the point (8,2)

Perpendicular Lines What do we know about perpendicular lines? Decide if the following are perpendicular Y=2x+2 Y=-2X+2 Y=(1/3)x-4 Y=3x+2 Y=4x-1 Y=4x-9 Y=(-1/4)x+4 Y=(4/1)x-9 Y=(-3/2)x+8 Y=x-1 Y=(2/3)x-2 Y=(-x)+5

Create a line perpendicular to… Create an equation for a line that is perpendicular to the line y=4x+1 that goes through the point (6,-2) What is the basic form of the equation? y = mx + b What does the slope have to be? m = -1/4 Do we know the y-intercept? Do we know y? x? y = -2 and x =6

Create a line perpendicular to… -2=(-1/4)(6)+B -2= -3/2 +B 4/3 = B Y=MX+B Y=(-1/4)X+(4/3)

Your Turn Find the equation of a line perpendicular to y + 3x = 1 that goes through the point (1, 4)