# How do you write the point slope form of the equation given (12,5) and m=-3?

Mar 20, 2017

$y - 5 = - 3 \left(x - 12\right)$

#### Explanation:

The point-slope form of the equation of the line is usually written in formula form as $y - {y}_{1} = m \left(x - {x}_{1}\right)$

To find a specific line, replace the m with the value for the slope, here m = -3, and the coordinates of the point using the given coordinates, $\left({x}_{1} , {y}_{1}\right) = \left(12 , 5\right)$.

Usually the brackets are removed and the equation rearranged.

Mar 20, 2017

$y = - 3 x + 41$

#### Explanation:

The slope form is:
$y = m x + b$
$m$ is already given:
$y = \left(- 3\right) x + b$
Since you know one solution to the equation, you can put those $x$ and $y$ values into the equation to solve for $b$:
$\left(5\right) = - 3 \left(12\right) + b$
Multiply $12$ and $- 3$:
$5 = - 36 + b$
Add $36$ to both sides:
$36 + 5 = b$
$41 = b$
Substitute $b$ into the slope formula and you're done:
$y = - 3 x + 41$