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