If is a line whose equation is y = 2x- 1, find the equation of the image of under each of the following translations:(x, y) S (x +3, y)

Answer 1

let (x,y) ---> (X,Y) where (X,Y) = (x+3,y)
so X = x+3
x = X-3 and y = Y

new equation:
Y = 2(X-3) - 1
Y = 2X - 7

or in the normal way : y = 2x - 7

test: take any two points on the original line, say
(0,-1) and (2,3)
after the translation
(0,-1) ---> (3,-1)
(2.3) ----> (5,3)

Do these new points lie on my new equation.
A quick mental check shows they are