Question

What is the equation of the line passing through `(13,7)` and `(4,2)`?

Answer 1

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

Explanation:

The Two Coordinate Equation
The general form of the two coordinate equation is `(y-y_1)/(y_2-y_1) = (x-x_1)/(x_2-x_1)` when you have the coordinates `(x_1,y_1)` and `(x_2,y_2)`.

Applied to Your Example
In your example `x_1 = 13`, `x_2 = 4`, `y_1 = 7` and `y_2 = 2`

Putting these values into the equation we get: `(y-7)/(2-7) = (x-13)/(4-13)`

Next we can simplify it by cleaning up the denominators of both fractions to get: `(y-7)/-5 = (x-13)/-9`

Rearranging into the form `y=mx+c`

To rearrange into this form we must first get rid of the fractions. To get rid of the first fraction we can multiply both sides by -5.

Doing this gives us `y-7 = (-5x+65)/-9`

To get rid of the second fraction we can multiply both sides by -9 to give us: `-9y+63 = -5x+65`

Next we can take away 63 from both sides to get y on its own: `-9y = -5x + 2`

Next we can divide by 9 to get `-y`: `-y = -5/9x + 2/9`

Finally we multiply by -1 to flip the signs: `y = 5/9x-2/9`