Question 989695
I'm assuming you meant to say "parallel to the line and it goes through (5,1)"


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Rule: Any two lines that are parallel have the same slope.


Using that rule above, we know that the parallel line has a slope of 2. This is because the slope of y = 2x-7 is 2 as well.


So m = 2 is the parallel slope


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The parallel line goes through (5,1) so x = 5 and y = 1.


We will plug m = 2, x = 5 and y = 1 into y = mx+b and solve for b


y = mx+b


y = 2x+b ... replace m with 2


y = 2*5+b ... replace x with 5


1 = 2*5+b ... replace y with 1, solve for b


1 = 10+b


1-10 = 10+b-10 ... Subtract 10 from both sides.


-9 = b


b = -9


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So we know that m = 2 and b = -9. Therefore the equation of the parallel line must be <font color="red">y = 2x - 9</font>


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Edit: Point slope form is y - y1 = m(x-x1). The line goes through (5,1) so (x1,y1) = (5,1)


y - y1 = m(x-x1) turns into y - 1 = 2(x - 5) when you plug in the given info. So the equation of the line in point slope form is y - 1 = 2(x - 5)


The equation of the line in slope intercept form is y = 2x-9. This can be found by following the steps shown above or by solving for y in y - 1 = 2(x - 5)