# How do you write the point slope form of the equation given (4,-5) and m=6?

Nov 15, 2017

$y = 6 x - 29$
graph{y=6x-29 [-10, 10, -5, 5]}

#### Explanation:

The formula to find the equation is $y = m x + b$

Since we know that $m = 6$, the equation we have so far would be $y = 6 x + b$.

Now, we will find $b$.

Plug in $\left(4 , - 5\right)$ where $x = 4$ and $y = - 5$

$- 5 = 6 \cdot 4 + b$

Switch sides:
$6 \cdot 4 + b = - 5$

Multiply the numbers:
$24 + b = - 5$

Subtract $24$ from both sides:
$24 + b \textcolor{red}{-} \textcolor{red}{24} = - 5 \textcolor{red}{-} \textcolor{red}{24}$

Simplify:
$b = - 29$

Therefore, the whole equation is:
$y = 6 x - 29$.

Nov 15, 2017

$y + 5 = 6 \left(x - 4\right)$

#### Explanation:

Remember that the point-slope form equation looks like this:

$y - k = m \left(x - h\right)$

Where $h$ and $k$ represents a point on the line and $m$ is the slope.

The point should have the coordinates like this: $\left(h , k\right)$

What we have to do is substitute the values in like so:

$y - k = m \left(x - h\right)$
$y - \left(- 5\right) = 6 \left(x - 4\right)$
$y + 5 = 6 \left(x - 4\right)$