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

1 Answer
Nov 11, 2015

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