For this case we have that by definition, the equation of a 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
On the other hand, we have that if two lines are parallel then their slopes are equal.
Given the line AB: [tex]y = 5x + 1,[/tex] the slope is [tex]m_ {1} = 5[/tex]
Therefore, a parallel line will have slope [tex]m_ {2} = 5.[/tex]
Thus, the equation is of the form is: [tex]y = 5x + b[/tex]
We substitute point[tex](4,5)[/tex]and find "b":
[tex]5 = 5 (4) + b\\5 = 20 + b\\5-20 = b\\b = -15[/tex]
Finally, a line parallel to line AB is: [tex]y = 5x-15[/tex]
Answer:
[tex]y = 5x-15[/tex]
