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What is an equation of the line that passes through the point (2,-5) and is parallel to the line x-2y=16

User Terseus
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1 Answer

5 votes

Answer: y=1/2(x)-6=0.5x-6

Step-by-step explanation: y=mx+c is the general equation of a straight line.

We are told that the line passes through the point (2, -5) this means at x=2 and y=-5

We need to substitute these into the general equation. This gives us the following:

y=mx+c

-5=m*2+c

To solve for c where the graph cuts the y -axis we need to -2m from both sides

-5-2m=2m-2m+c

-5-2m=c

Places this back into the general equation of a straight line gives us the following

y=mx-5-2m

this is the same as

y=m(x-2)-5........we take out a common factor of m

Now we want the above line to be parallel to x-2y=16

To see this we must put the above equation into the form y=mx+c

x-2y=16

We need to make y the subject that is solve for y or have y on its own

To get y term on its own we need to subtract x from both sides

x-x-2y=16-x

-2y=16-x

To finally get y on its own we need to divide both sides by -2

-2y/-2=16/-2 -x/-2

y=-8+x/2

y=x/2-8

this is the same as

y=1/2(x)-8

Therefore m=1/2

we now substitute this back into the previous original equation to get the following

y=1/2(x-2)-5

y=1/2(x)-1-5

y=1/2(x)-6

User Alexey Usachov
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