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Write the equation of a perpendicular and parallel line to the following: (in picture)

Write the equation of a perpendicular and parallel line to the following: (in picture-example-1
User Codinguser
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anIf we have an equation of the form


y=mx+b

then the equation of the perpendicular will be


y=-(1)/(m)x+c

where c is any arbitrary constant determined by the point the line must pass through,

Now in our case, we have


y=-10x+20

Therefore, the equation of the perpendicular line will be


y=(1)/(10)x+c

We must choose c such that the above line passes through (-2,2).

Putting in y = 2 and x = 2 from (-2, 2) gives


2=(1)/(10)(-2)+c
2=-(1)/(5)+c
\therefore c=(11)/(5).

Hence, the equation of a line perpendicular y = -10x + 20 and passing through (-2, 2) is


y=(1)/(10)+(11)/(5)

Now we find the equation of a line parallel to y = -10x+20 and passing through (-2,2).

Now, the slope of the parallel line is the same as that of the original equation; therefore the equation for the parallel line we have is


y=-10x+k

We find k by using the point (-2,2) and substituting x = -2 and y = 2 into the above equation to get


2=-10(-2)+k
2=20+k
\therefore k=-18.

Hence, the equation of the parallel line is


y=-10x-18

User Alex Leach
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