Answer:
[tex]\sf y = \dfrac{5}{2}x +\dfrac{17}{2}[/tex]
Step-by-step explanation:
[tex]\sf y =\dfrac{5}{2}x+1[/tex]
m= 5/2
Parallel lines have same slope.
Slope y-intercept form: y = mx +b
Here, m is the slope and b is the y-intercept
[tex]\sf y = \dfrac{5}{2}x + b[/tex]
Point (-3,1) passes through the required line. Substitute (-3,1) in the above equation and find 'b'.
[tex]\sf 1 = \dfrac{5}{2}*(-3)+b\\\\1 =\dfrac{-15}{2}+b\\\\[/tex]
[tex]\sf 1 +\dfrac{15}{2}=b\\\\\dfrac{2+15}{2}=b\\\\\\ \boxed{b= \dfrac{17}{2}}[/tex]
[tex]\sf \bf y = \dfrac{5}{2}x+\dfrac{17}{2}[/tex]