I've tried this and I'm really confused and I wanted to see if I got the right answer

Question

The question was: Write an equation of a line passing through (2,5)

that is parallel to y = 3x +1

The answer I got was:

y + 2 = 3(x + 5) which is the same as y = 3x + 13

Answer 1

So, a point is written as (x,y) and the formula is...

y - y₁ = m(x - x₁)

y - 5 = 3(x - 2)

y - 5 = 3x - 6

y = 3x - 1

Want to check your answer?

5 = 3(2) - 1

5 = 6 - 1

5 = 5

Boom.

Another way to do it...

y = mx + b

5 = 3(2) + b

5 = 6 + b

b = -1

y = 3x - 1

Answer 2

You have the x and y coordinates reversed and signs wrong:

y-5 = 3(x-2)

y -5 = 3x - 6

y = 3x - 1