Question

# The equations of three lines are given below Line 1: y=3x-5 Line 2: y=-1/3x +1 Line...

The equations of three lines are given below Line 1: y=3x-5 Line 2: y=-1/3x +1 Line 3: 3x-9y=18 For each pair of lines, determine whether they are parallel, perpendicular, or neither: 1. Line 1 and 2 are they (parallel, perpendicular, or neither.) 2. Line 1 and 3 are they (parallel, perpendicular, or neither.) 3. Line 2 and 3 are they (parallel, perpendicular, or neither.

Solution :

Line 1: y=3x-5

Line2 : y=-x/3+1

Line3 : 3x-9y=18==>y=x/3-2

Now comparing with equation

y=mx+c , where m is slope of Line, c is y-intercept

So

Slope of Line 1 say m_1=3

Slope of Line 2 say m_2 =-1/3

Slope of Line 3 say m_3 =1/3

Result 1) Two lines are parallel if they have same slopes

Result 2) Two lines are y=mx+c and y=m'x+c are perpendicular if mm'=-1

now m_1.m_2=-1===>line L_1 and L_2 are perpendicular

Line L_1 and L_3 are Neither parallel nor perpendicular {as their slopes are not equal and product of slopes is not equal to -1}

Lines L_2 and L_3 are Neither parallel nor perpendicular {as their slopes are not equal and product of slopes is not equal to -1}

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