Question

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

Answer 1

`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`.