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#