How Do You Change From Slope-intercept Form To Standard Form?

Where a, b, and c are integers.

Slope-intercept form has
y = mx + b

To convert slope-intercept form to standard form, subtract mx from both sides of the equation.
-mx + y = b

If m is a fraction, multiply the equation by its denominator.

Example
y = 2/3x + 6    (slope-intercept form)
-2/3x + y = 6    (after the subtraction of 2/3x)
-2x + 3y = 18    (standard form, after multiplication by 3)
thanked the writer.
Standard form has
ax + by = c, where a, b, and c are integers.

Slope-intercept form has
y = mx + b

To convert slope-intercept form to standard form, subtract mx from both sides of the equation.
-mx + y = b

If m is a fraction, multiply the equation by its denominator.

Example
y = 2/3x + 6    (slope-intercept form)
-2/3x + y = 6    (after the subtraction of 2/3x)
-2x + 3y = 18    (standard form, after multiplication by 3)
thanked the writer.
Oddman commented
You are correct. My mistake. 3y - 2x = 18 would be in standard form. The requirement is that the leading coefficient be non-negative.
Kenjay Reyes commented
Yeah but i am wondering,....what's the given in the problem?
Oddman commented
The given in the problem is "slope-intercept form." There can be many variations on slope-intercept form, so an example was chosen that was intended to illustrate some of the issues involved in changing to standard form. I find a generic answer is often more understandable if it comes with a specific example.
Ok so let's start out easy. The problem is y=5-3X. In this equation, you simply add 3x to each side.
Y+3x=5.
Now we get a little bit harder.
Y=3x-9. First, you can subtract 3x from each side.
-3x+y=9. To get the real standard form, you multiply each side by -1.
So, 3x-1y=9. That's your standard form.
thanked the writer.
Slope intercept form is
y = mx + b
Standard form is
ax + by = c
where the leading coefficient (a) is positive. The coefficients a, b, and c are relatively prime integers.

To get from slope-intercept form to standard form you can subtract y+b from both sides. This will give you
-b = mx - y
You can rearrange this to
mx - y = -b
Multiply by the least common denominator of m and b, and multiply by -1 if m is negative. Divide any common factors from all of the coefficients.
thanked the writer.