For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cut-off point with the y axis
We have the following line:
[tex]y = 2x-8[/tex]
The slope is [tex]m_ {1} = 2[/tex]
By definition, if two lines are parallel then their slopes are equal. Thus, a line parallel to the given line will have a slope[tex]m_ {2} = 2[/tex]
Therefore, the equation of the parallel line will be of the form:
[tex]y = 2x + b[/tex]
We substitute the given point and find "b":
[tex]3 = 2 (-1) + b\\3 = -2 + b\\3 + 2 = b\\b = 5[/tex]
Finally, the equation is:
[tex]y = 2x + 5[/tex]
Answer:
[tex]y = 2x + 5[/tex]
