For linear function world problems, I have no trouble finding the slope. What I would like to know is when you look for the y intercept how do you know when you should use the point slope form?
You should be familiar with a method to change one form to another.
e.g. 3x + 4y = 9 <-----> y = (-3/4)x + 9/4
suppose you have a fractional slope. In that case I would almost always use the point slope form. E.g. slope = -3/5, point is (4,-3)
Using the point slope form:
y+3 = (-3/5)(x-4)
multiply both sides by the denominator of the slope, this will clear your fraction
5y + 15 = -3(x-4)
5y + 15 = -3x + 12 ---> re-arrange to get a positive x at the front of the left side
3x + 5y = -3 , done
You might want to "memorize" the following
For Ax + By = C, the slope = -A/B
the x-intercept is C/A, (I mentally let y = 0)
the y-intercept is C/B, (I mentally let x = 0)
Another quickie:
If you have an equation written as
x/a + y/b = 1, then the x-intercept is a, and the y-intercept is b
e.g.
suppose you have x/3 + y/5 = 1
multiply by 15
5x + 3y = 15
from what I said above, the x intercept is 15/5 or 3
and the y-intercept is 15/3 = 5
notice in my given equation, a = 3 and b = 5