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

Jun 28, 2017

$y = - x + 9$ or $y = 9 - x$

#### Explanation:

First, we need to find the gradient of the line. $m = \text{change in y"/"change in x}$. 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: $m = \frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

Now, we have value which we can put in: $m = \frac{11 - 9}{- 2 - 0} = \frac{2}{-} 2 = - \left(\frac{2}{2}\right) = - 1$.

The equation of a line can be found using either of our set of coordinates, where either:
$y - {y}_{1} = m \left(x - {x}_{1}\right)$, or
$y - {y}_{2} = m \left(x - {x}_{2}\right)$

I will be putting (0,9) in so:
$y - {y}_{1} = m \left(x - {x}_{1}\right)$
$y - 9 = - 1 \left(x - 0\right)$
$y - 9 = - 1 \left(x\right)$
$y = - x + 9$

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