Question

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

Answer 1

`x-4y=-6`

Explanation:

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

The standard form of a linear equation is

`ax+by=c`

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

You can also get the standard form by moving the `mx` to the left side in slope-intercept form.

`y=mx+b->-mx+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:

`(3-2)/(6-2)=1/4`

The slope is `1/4`.

Now you have `y=1/4x+b`

To find `b`, plug in any point. You are given `(2,2),(6,3)`.

`2=1/4*2+b=>2=2/4+b=>3/2=b` or

`3=1/4*6+b=>3=3/2+b=>3/2=b`

Either way, you'll get `3/2` as `b`.

Now, write out what you have:

`y=1/4x+3/2`

Convert to standard form:

`-1/4x+y=3/2`

`-4(-1/4x+y=3/2)`

`x-4y=-6`