# How do you write the equation of a line in slope intercept, point slope and standard form given Point: (5,-8) and is parallel to y=9x+4?

Jul 19, 2018

Slope intercept form of the equation is $y = 9 x - 53$, point slope form is $y + 8 = 9 \left(x - 5\right)$, and standard form is $- 9 x + y = - 53$

#### Explanation:

Lines that are parallel have the same slope. Knowing this, the slope is $9$, so $m = 9$ in each of the forms

Slope intercept form: $y = m x + b$

First plug in the slope:

$y = 9 x + b$

Next we have to solve for $b$ which is done by plugging in the point that was given $\left(5 , - 8\right)$ for $x$ and $y$:

$- 8 = 9 \left(5\right) + b$

$- 8 = 45 + b$

$b = - 53$

Now that we know b, we can plug it in to the slope intercept form, giving us $y = 9 x - 53$

Point slope form: $y - {y}_{1} = m \left(x - {x}_{1}\right)$

Plug in the slope, which is $9$

$y - {y}_{1} = 9 \left(x - {x}_{1}\right)$

Plug the point that is given, $\left(5 , - 8\right)$, into the point slope form:

$y - \left(- 8\right) = m \left(x - \left(5\right)\right)$

Simplify, giving you the final answer for point slope form:

$y + 8 = 9 \left(x - 5\right)$

Finally, standard form which is $a x + b y = c$

To get standard form we can use slope intercept form which we know is

$y = 9 x - 53$

Subtract $9 x$ from both sides, giving you standard form:

$- 9 x + y = - 53$