What is the equation of the line passing through (41,89) and (1,2)?

1 Answer
Nov 11, 2015

Use the two coordinate formula and rearrange into the form y=mx+c

Explanation:

The Two Coordinate Formula
The general form of the two coordinate formula is:

(y-y_1)/(y_2-y_1) = (x-x_1)/(x_2-x_1)

when you have two coordinates, (x_1,y_1) and (x_2,y_2).

Applied to your example
The values in your example are: x_1 = 41, x_2 = 1, y_1 = 89 and y_2 = 2

Substituting these into the formula we get:

(y-89)/(2-89) = (x-41)/(1-41)

If we evaluate the denominators we get:

(y-89)/-87 = (x-41)/-40

We can then multiply both sides by -87 to get rid of one fraction:

y-89 = (-87x+3567)/-40

Next we can multiply both sides by -40 to get rid of the other fraction:

-40y+3560 = -87x+3567

Next we can take away 3560 from both sides to get -40y on its own:

-40y = -87x+7

Next we can multiply by -1 to flip the signs:

40y = 87x-7

Finally we divide by 40 to get y on its own and our answer in the form y=mx+c:

y = 87/40x-7/40