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

Nov 11, 2015

Use the two coordinate formula and rearrange into the form $y = m x + c$

#### Explanation:

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

$\frac{y - {y}_{1}}{{y}_{2} - {y}_{1}} = \frac{x - {x}_{1}}{{x}_{2} - {x}_{1}}$

when you have two coordinates, $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$.

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:

$\frac{y - 89}{2 - 89} = \frac{x - 41}{1 - 41}$

If we evaluate the denominators we get:

$\frac{y - 89}{-} 87 = \frac{x - 41}{-} 40$

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

$y - 89 = \frac{- 87 x + 3567}{-} 40$

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

$- 40 y + 3560 = - 87 x + 3567$

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

$- 40 y = - 87 x + 7$

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

$40 y = 87 x - 7$

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

$y = \frac{87}{40} x - \frac{7}{40}$