Determine the inverse of the given equation: x - 2y = 5I have to graph the inverse, which is not a problem, but in case you needed to know that to answer, i thought i might let you know :)

Expert Answers
hala718 eNotes educator| Certified Educator

x - 2y = 5

First we need to rewrite the equation:

First subtract x ffrom both sides:

-2y = -x+5

Now divide by -2

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

Now to find the inverse we will rewrite again in x terms.

Multiply by 2:

==> 2y = x - 5

Now add 5 to both sides:

==> 2y + 5 = x

==> x = 2y + 5

Then the inverse y^-1 is:

y^-1 = 2x + 5

neela | Student

We will plot graph x-2y= 5 for any  3 points

x =   5 ,   y = (x-5)/2 =  (5-5)/2  = 0

x =  15 , y  = (15- 5)/2  = (15 -5)/2 = 5.

x = 25 , y = (25-5)/2 = 10

Therefore ( 5,0)   (15,5), and (25, 10 ) are the points on x-2y = 5.

Therefore (0,5) and (5,15)  and (10,25)  should be  the points on the inverse graph.

The  line passing through (0,5) and (5,15) is

y-5 =  [(15-5)/5](x-0) by standard formula.

y-5 = 2x. or

2x-y  = -5 is the inverse of x-2y = 5.

y-5 = 2x

2x-y = 5 is the graph of the inverse of  x-2y = 5.

Verification:

Now  if (a,b) is a point on x-2y = 5, then (b,a) is a  point on 2x-y =5.

Since (a, b) on x-2y = 5,  a -2b = 5. Or (b,a) verifies 2x -y = -5 as

2b-a = -(a-2b) = -5.