3. a. Find the equation of the line that passing through the point (-1,6) and pe

Question

3. a. Find the equation of the line that passing through the point (-1,6) and perpendicular to b. Find the equation of the line that passing through the point (1,6) and parallel to the line c. Find the equation of the line that passing through the point (0,3) and parallel to the line d. Find the equation of the line that passing through the point (2,4) and perpendicular to the e. Find the equation of the line that passing through the point (-3,1) and perpendicular to the line 2x+ 2y+10-0 x+ 2y 6 2x+ 2y + 10 0 line 2x+ 2y 10-0 the line x+ 2y 15 0

Explanation / Answer

slopes of parallel lines are equal . product of slopes of perpendicular lines is -1

3)

a)given line 2x+2y +10=0

=>2y =-2x-10

=>y=-1x-5

slope of given line =-1

so slope of perpendicular line = 1

equation of perpendicular line with slope 1 and passing through (-1,6):

=>y-6=1(x-(-1))

=>y-6=x+1

=>-x+y=7

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b)

given line x+2y =6

=>2y =-x+6

=>y=-(1/2)x+3

slope of given line =-(1/2)

so slope of parallel line = -(1/2)

equation of parallel line with slope -(1/2) and passing through (1,6):

=>y-6=-(1/2)(x-1)

=>2(y-6)=-(x-1)

=>2y-12=-x+1

=>x+2y=13

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c)

given line 2x+2y +10=0

=>-2y =2x+10

=>y=-1x+5

slope of given line =-1

so slope of parallel line = -1

equation of parallel line with slope -1 and passing through (0,3):

=>y-3=-1(x-0)

=>y-3=-x

=>x+y=3

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d)given line 2x+2y +10=0

=>2y =-2x-10

=>y=-1x-5

slope of given line =-1

so slope of perpendicular line = 1

equation of perpendicular line with slope 1 and passing through (2,4):

=>y-4=1(x-2)

=>y-4=x-2

=>-x+y=2

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e)given line x+2y -15=0

=>2y=-x+15

=>y=-(1/2)+(15/2)

slope of given line =-(1/2)

so slope of perpendicular line = 2

equation of perpendicular line with slope 2 and passing through (-3,1):

=>y-1=2(x-(-3))

=>y-1=2(x+3)

=>y-1=2x+6

=>-2x+y=7

PLEASE RATE IF HELPFUL.PLEASE COMMENT IF YOU HAVE ANY DOUBT

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