# What is the equation of the line passing through (6,6) and (1,2)?

Nov 11, 2015

Using the Two Coordinate Equation

#### Explanation:

The Two Coordinate Equation
The two coordinate equation's general form is written as: $\frac{y - {y}_{1}}{{y}_{2} - {y}_{1}} = \frac{x - {x}_{1}}{{x}_{2} - {x}_{1}}$ where you have the coordinates $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$.

In your case ${x}_{1} = 6$, ${x}_{2} = 1$, ${y}_{1} = 6$ and ${y}_{2} = 2$.

If we put these values into the equation we get:
$\frac{y - 6}{2 - 6} = \frac{x - 6}{1 - 6}$

Now we need to rearrange into the form $y = m x + c$

First simplify the denominator of both fractions to get:
$\frac{y - 6}{-} 4 = \frac{x - 6}{-} 5$

Next multiply both sides by -4 to get:

$y - 6 = \frac{- 4 x + 24}{-} 5$

Now multiply both sides by -5 to get rid of the other fraction:

#-5y+30 = -4x+24

Next we take away 30 from both sides to get $y$ on its own:
$- 5 y = - 4 x - 6$

Now multiply by -1 to change the signs:

$5 y = 4 x + 6$

Lastly divide by 5 to get a single $y$

$y = \frac{4}{5} x + \frac{6}{5}$