Given:
The point is (-2,3).
The parallel line is y=4x+2.
This is of the form
[tex]y=mx+b_1[/tex]
where slope m=4.
We know that the slope of the parallel lines is equal.
Thus we get the slope m =4 for the required line.
Consider the line equaiton
[tex]y=mx+b[/tex]
Substitute x= -2,y=3, and m =4 in the equation to find the value of b.
[tex]3=4(-2)+b[/tex]
[tex]3=-8+b[/tex]
Adding 8 on both sides of the equation, we get
[tex]3+8=-8+b+8[/tex]
[tex]11=b[/tex]
We get b=11.
Substitute m=4 and b=11 in the equation, we get
[tex]y=4x+11[/tex]
Hence the line equation that passes through the point (-2,3) and parallel to y=4x+2 is
[tex]y=4x+11[/tex]
