Slope and Changes in X I'm working on a question where I got the second part of it but not the first. The second part asks to prove a y-intercept given y= # and x= #. I got the answer for that, but I'm stuck on the first part in terms of I'm not sure what it's asking!
The question says:
The graph y= f(x) is a straight line with slope -2/3. If x changes by -12 what is the change in f(x)?
Is this a translation, where the line is moving -12 places? Or something else?
Thanks in advance!
 A: Just as a review of the basic ideas to do with functions conceptually, I'll review intercept and slope:
The two most emphatic elementary concepts held within the function are termed: the slope  and the intercept . Both slope and intercepts can be found graphically or algebraically and both methods are valuable within their own realms when attempting to extrapolate information from a particular function. The ‘x’ and ‘y’ intercepts can be determined algebraically by setting the opposite variable of which intercept is sought to zero and proceeding to solve for the variable whose intercept is sought. That is to say, if the ‘x’ intercept is required, then the equation is set to equal to zero signifying that the function is to calculate the desired value for ‘x’ as an output for when the value of ‘y’ is zero. The primary method for finding the slope of a linear function is by determining, graphically, the ratio of ‘y’-values to ‘x’-values (∆y/∆x)  over a specified interval.
In practice as in for your question, given a slope of $\frac{-2}{3}$, a change in the x coordinate by -12, will give you a change in $f(x)$ (also known as the y-coordinate, or the output of the function) of what? So, you can simply set up a ratio if you don't see immediately what to do.
$$\frac{-2}{3} = \frac{∆f(x)}{12}$$
Resultantly, $∆f(x) = -8$.
