Answer:
[tex]\large\boxed{y=\dfrac{1}{4}x-3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
Parallel lines have the same slope. Therefore if given line is
[tex]y=\dfrac{1}{4}x+2[/tex]
then the slope of our line is [tex]m=\dfrac{1}{4}[/tex].
We have the equation:
[tex]y=\dfrac{1}{4}x+b[/tex]
The line passes through (4, -2). Put the coordinsted pf the point to the equation:
[tex]-2=\dfrac{1}{4}(4)+b[/tex]
[tex]-2=1+b[/tex] subtract 1 from both sides
[tex]-3=b\to b=-3[/tex]
Finally:
[tex]y=\dfrac{1}{4}x-3[/tex]
