Question

What is the equation of the line that goes through `(-1, 4)` and is parallel to `y = 3x - 3`?

Answer 1

`y=3x+7`

Explanation:

Finding an equation of the line that is parallel to another line simply means that both would not intersect, so by these we can say that their slope must be equal, if the slope are not equal, they would intersect

In the linear equation
`y=mx+b`
`m` is the slope of the line

So from your given
`y=3x-3`
We can conclude that `m=3` so its slope is 3

Then finding the equation where the points`(a,b)` and the slope`(m)` are given
`(y-b)=m(x-a)`

So to answer your phone question,
Given point `(-1,4)` and `m=3`
By the substituting the values to the formula for finding the equation of the line
We will have
`(y-4)=3(x-(-1))`, simplify it
`(y-4)=3(x+1))`
`y-4=3x+3`
`y-4+4=3x+3+4`
`y=3x+7`

So the equation of the line that is parallel to `y=3x+3` passing throught the point (-1,4) is `y=3x+7`