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
On the other hand, we have that if two lines are parallel then their slopes are equal.
We have the following equation of the line:
[tex]3x-y = 5[/tex]
Rewriting we have:
[tex]y = 3x-5[/tex]
Thus, the slope of the lines is [tex]m_ {1} = 3[/tex]
Then, a parallel line will have slope [tex]m_ {2} = 3[/tex]
Thus, the equation of the new line will be given by:
[tex]y = 3x + b[/tex]
To find the cut-off point "b", we substitute the point through which the line passes:
[tex]-2 = 3 (-1) + b\\-2 = -3 + b\\-2 + 3 = b\\b = 1[/tex]
Finally the equation is:
[tex]y = 3x + 1[/tex]
ANswer:
[tex]y = 3x + 1[/tex]
