How do you write the equation of a line in point slope form into slope intercept form given #y - -1/4 = -3(x + 1/4)#?

First you have to put your point slope form equation into a correct point slope form.
This being,

#y + 1/4 = -3(x + 1/4)#

I added a plus sign to #y + 1/4# because two negatives equal a positive.

Now that you have your correct point slope form you can solve for your slope intercept form.

First, you want to eliminate the bracket(s). In this situation, you much multiply everything by -3 to eliminate the bracket.

Your equation will now look like this.

#y + 1/4 = -3x -3/4#

Next step is isolating the y variable. In other words, getting y by itself. (y=...)

For this equation, you must subtract 1/4 to cancel out the positive 1/4. But remember everything you take away from one side, it must be done to the other side. This means you will have to add a -1/4 to the end of the equation.

Your equation will look like this:

#y + 1/4 - 1/4= -3x -3/4 -1/4#

Which will end up like this

#y= -3x -3/4 -1/4#

Last step is to combine like terms, which in this case would be regular numbers or fractions.

Once you have done that, you know have your slope intercept form, which will look like this=

#y= -3x -1#