Question

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

Answer 1

Using the Two Coordinate Equation

Explanation:

The Two Coordinate Equation
The two coordinate equation's general form is written as: `(y-y_1)/(y_2-y_1) = (x-x_1)/(x_2-x_1)` where you have the coordinates `(x_1,y_1)` and `(x_2,y_2)`.

Applied to Your Example
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:
`(y-6)/(2-6) = (x-6)/(1-6)`

Now we need to rearrange into the form `y=mx+c`

First simplify the denominator of both fractions to get:
`(y-6)/-4 = (x-6)/-5`

Next multiply both sides by -4 to get:

`y-6 = (-4x+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:
`-5y = -4x-6`

Now multiply by -1 to change the signs:

`5y = 4x+6`

Lastly divide by 5 to get a single `y`

`y = 4/5x + 6/5`