Converting Y=mx+b to standard form

Question

I need to convert slope-intercept form to standard for for my next test.
For example:

Convert 60x + 30y=15
First, I subtract 30y.

-30y = 60x + 15

Then, I divide by -30.

y = -2x - (1/2)

This is where I am confused. Would the (1/2) be negative or positive?

Answer 1

Dividing both sides of 60x + 30y = 15 by 15:

4x + 2y = 1

This is in the "Standard Form" of the linear equation.

 

"Slope-Intercept Form" is y = mx + b, where m is the slope and b is the y-intercept.

 

Subtract 4x from both sides:

4x - 4x + 2y = 1 - 4x

Divide both sides by 2:

y = 1/2 - 2x or y = -2x + 1/2

The slope is -2 and the y-intercept is 1/2.

 

Standard Form can represent any line, including x = 3, a vertical line. Slope-Intercept Form cannot represent a vertical line, but otherwise it's very useful for generating points to graph. Just start by graphing the y-intercept point, (0,b), then use the slope to create another point, and another, ...

Answer 2

Hi Ben,

I believe that the confusion comes from a simple mistake made early on when trying to solve this problem.

The problem is that you want your equation in a y = mx + b format, if I'm not mistaken.

Your example is:
60x + 30y = 15

If you subtract the term with y as you suggest, you should get:
60x = 15 - 30y

Then in order to isolate the term with y, you would need to subtract 15 from both sides to give:
60x - 15 = -30y

Now in order to "solve for y", you would divide by negative 30 to give you the final answer:
-2x + 1/2 = y


An easier way to solve this is to subtract the term 60x in the first place to get y alone, and then divide by positive 30.

Hope that this was helpful, and good luck in your work.
Joseph

Answer 3

I apologize, I missed the error in the first step.