Parallel lines have the same slope.
We have [tex]y=\dfrac{1}{2}x-7[/tex].
Therefore we have [tex]y=\dfrac{1}{2}x+b[/tex]
We must find b. We know, the line passes through (-3, -2).
Substitute the values of point to the equation of the new function:
[tex]-2=\dfrac{1}{2}(-3)+b\\\\-2=-1.5+b\qquad|\text{add 1.5 to both sides}\\\\-0.5=b\to b=-0.5\to b=-\dfrac{1}{2}[/tex]
Answer: [tex]y=\dfrac{1}{2}x-\dfrac{1}{2}[/tex]
