How do you change an equation into slope intercept form?

just rearrange and make y as subject

x + 3y = 7

subtract x from both sides

3y = -x + 7

divide by 3

y = -(1/3)x + 7/3

Very simple
x + 3y = 7
subtract the x to the other side
3y = -x + 7
divide by 3
y = (-x +7)/3 or you can put it your way y = -x/3 + 7/3

3x + 2y = 10
subtract 3x to other side
2y = -3x + 10
divide by 2
y = -3x/2 + 5      (10/2) = 5

x + 2y = 2
subtract x
2y = x+2
divde by 2
y = x/2 + 1      (2/2) = 1

3x+2y=10 would be y= -3/2x +5

x+2y=2 the slope intercept form is y= -1/2x +1

The way you solve  x+3y=7 is first bring over the x by subtracting.

You now have 3y= -x+7, Then divide both sides by 3 and you get the answer y=-1/3x+7/3

you must solve for y, or get it by itself... this means to get y= (something).

I will show the work and then explain it...

x+3y=7                    There are 2 terms on the left side of this equation
-x       -x                   you need to put the x on the other side so now    
                                 it is just the y on the left side.
3y= - x + 7           here the x is negative because you subtracted it
/3        /3               now you must divide by 3 to get y by itself
y= -1/3x +7/3         make sure each term on the left is divided by 3.


I hope this helps.