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Parallel lines have exactly the same slope. Therefore, to find the slope of a parallel line, we need to know the slope of the given line.

We can calculate it by substituting points that lie on the given line into the slope formula. Let's use $(-3,0)$ and $(3,2).$$m=x_{2}−x_{1}y_{2}−y_{1} $

$m=3−(-3)2−0 $

Simplify right-hand side

$m=31 $

$y=mx+b$

SubstituteValuesSubstitute values

$2=31 ⋅1+b$

Solve for $b$

MultByOne$a⋅1=a$

$2=31 +b$

SubEqn$LHS−31 =RHS−31 $

$2−31 =b$

RearrangeEqnRearrange equation

$b=2−31 $

NumberToFrac$a=33⋅a $

$b=33⋅2 −31 $

MultiplyMultiply

$b=36 −31 $

SubFracSubtract fractions

$b=35 $

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