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

1 Answer
Feb 24, 2018

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