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's the slope
b: It is the cut-off point with the y axis
By definition, if two lines are parallel then their slopes are equal. A line parallel to[tex]y = -3x + 1[/tex], will have the same slope -3. Thus, the equation will be of the form:
[tex]y = -3x + b[/tex]
We substitute the given point and find "b":
[tex]2=-3(4)+b\\2=-12+b\\2+12=b\\b=14[/tex]
Finally, the equation is:
[tex]y = -3x + 14[/tex]
Answer:
[tex]y = -3x + 14[/tex]
