How does one find the change?

Question

I tried using ratios but I failed. I need to subtract one to get the correct answer. I remember finding the change before, but I've forgotten how to. Any hints?

Answer 1

Just use two of the coordinates in the diagram to solve for $m$ and $b$. For example, you can make the two equations $$3 = -2m+b\\-3=m+b$$ Subtracting the second equation from the first results in $$(3-(-3))=m(-2-1)+(b-b) \\ \implies 6 = -3m \\ \implies m = \frac{-1}{2}$$

Now plug in $m$ into either of the two equations above to solve for $b$. Once you know $b$ and $m$, you can solve $y=4m+b$ for $y$.