Answer:
[tex]y=5x+7[/tex]
Step-by-step explanation:
step 1
Find the slope of the line parallel to the given line
we know that
If two lines are parallel, then their slopes are equal
The equation of the given line is [tex]y=5x+4[/tex]
The slope of the given line is [tex]m=5[/tex]
so
The slope of the line parallel to the given line is also [tex]m=5[/tex]
step 2
Find the equation of the line parallel to the given line
The equation of the line in point slope form is
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=5[/tex]
[tex]point\ (-1,2)[/tex]
substitute
[tex]y-2=5(x+1)[/tex]
step 3
Convert to slope intercept form
Isolate the variable y
[tex]y-2=5x+5[/tex]
[tex]y=5x+5+2[/tex]
[tex]y=5x+7[/tex]
