How do you write the point slope form of the equation given (0,9) and (-2,11)?

1 Answer
Jun 28, 2017

#y=-x+9# or #y=9-x#

Explanation:

First, we need to find the gradient of the line. #m="change in y"/"change in x"#. I will make (0,9) the first set of coordinates, where #x_1# = 0, and #y_1# = 9.

Then I will male the second set of coordinates (-2, 11) where #x_2# = -2, and #y_2# = 11.

The gradient can also be written like this: #m= (y_1-y_2)/(x_1-x_2)=(y_2-y_1)/(x_2-x_1)#.

Now, we have value which we can put in: #m=(11-9)/(-2-0)=2/-2=-(2/2)=-1#.

The equation of a line can be found using either of our set of coordinates, where either:
#y-y_1=m(x-x_1)#, or
#y-y_2=m(x-x_2)#

I will be putting (0,9) in so:
#y-y_1=m(x-x_1)#
#y-9=-1(x-0)#
#y-9=-1(x)#
#y=-x+9#

The equation of the line is #y=-x+9# or #y=9-x#.