First we find the slope of the given line as both the lines are parallel therefore their slopes are equal.
To find slope of given line we compare the equation with point slope form i.e.
[tex]y=mx+c[/tex]
On comparing [tex]y=2x+9[/tex]
We get [tex]m=9=slope [/tex]
As the required line is parallel to given line its slope is equal to given line
[tex]m=9[/tex]
Required line pass through[tex](3,1)[/tex]
Using point slope form
[tex]y-y_1=m(x-x_1)[/tex]
Here [tex]m=9, y_1=1, x_1=3[/tex]
Putting the values and solving
[tex]y-1=9(x-3)[/tex]
[tex]y-1=9x-27[/tex]
[tex]9x-y=26[/tex] is the required equation
Hope this will help
