Find the equation of the image of a line y=3x-8 after reflection over the x-axis

The required image line is 3x + y = 8

Step-by-step explanation:

We have to find two points on the given straight line then find their reflection points over the x-axis and then finally the straight line passing through those two image points will give the required straight line.

Now, the given straight line is y = 3x - 8.

Now, two any points on this straight line are say (1,-5) and (2,-2).

So, the image of (1,-5) point reflecting over the x-axis will be (1,5) and the image of the point (2,-2) reflecting over the x-axis will be (2,2).

Therefore, the straight line passing through those two image points will have equation  

⇒ y - 5 = 3(1 - x)

⇒ y - 5 = 3 - 3x

⇒ 3x + y = 8

Hence, the required image line is 3x + y = 8 (Answer)