For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We have to, if two lines are parallel then their slopes are equal.
Given the line [tex]y = x + 4[/tex], with slope[tex]m_ {1} = 1[/tex]. A parallel line will have slope [tex]m_ {2} = 1[/tex]and its equation will be of the form:
[tex]y = x + b[/tex]
We substitute the given point and find "b":
[tex]2 = 2 + b\\2-2 = b\\b = 0[/tex]
Finally, the equation is:
[tex]y = x[/tex]
Answer:
[tex]y = x[/tex]
