# How do you write an equation in standard form given (2, 2) and (6, 3)?

Feb 24, 2018

$x - 4 y = - 6$

#### Explanation:

I'm assuming that this is a linear equation...

The standard form of a linear equation is

$a x + b y = c$

where $a$ is non-negative and an integer.

You can also get the standard form by moving the $m x$ to the left side in slope-intercept form.

$y = m x + b \to - m x + y = b$

First, find the slope-intercept form by finding the slope:

"slope"=(Δy)/(Δx) or (y_2-y_1)/(x_2-x_1)

Plug in:

$\frac{3 - 2}{6 - 2} = \frac{1}{4}$

The slope is $\frac{1}{4}$.

Now you have $y = \frac{1}{4} x + b$

To find $b$, plug in any point. You are given $\left(2 , 2\right) , \left(6 , 3\right)$.

$2 = \frac{1}{4} \cdot 2 + b \implies 2 = \frac{2}{4} + b \implies \frac{3}{2} = b$ or

$3 = \frac{1}{4} \cdot 6 + b \implies 3 = \frac{3}{2} + b \implies \frac{3}{2} = b$

Either way, you'll get $\frac{3}{2}$ as $b$.

Now, write out what you have:

$y = \frac{1}{4} x + \frac{3}{2}$

Convert to standard form:

$- \frac{1}{4} x + y = \frac{3}{2}$

$- 4 \left(- \frac{1}{4} x + y = \frac{3}{2}\right)$

$x - 4 y = - 6$