Write an equation in standard form for a line that passes through (4,1) & (5,7)

Y = mx + b

First equation 1 = m(4) + b, bring everything to one side m(4) + b - 1 = 0
Second equation 7 = m(5) + b, bring everything to one side m(5) + b - 7 = 0

Set them equal to each other, 

m(4) + b - 1 = m(5) + b - 7

If you bring the b over to the left hand side it becomes

m(4) + b - b - 1 = m(5) - 7

m(4) - 1 = m(5) - 7

Solve for m

6 = m

Plug m = 6 into either equation from the beginning,

m(4) + b - 1 = 0

6(4) + b - 1 = 0

24 + b - 1 = 0

b = -23

Knowing m and b we can now make an equation

y = mx + b

y = 6x -23 Final answer

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