# 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!

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It means: if you have a point on the line $(x,y)$ and you shift $x$ by $-12$, how much must you also shift the $y$ coordinate for the destination point to be on the line as well? You can use geometry to intuitively help you solve this by drawing a right triangle with the hypotenuse as part of the line and base length 12. Also, I don't think negative exponents are relevant here. – anon Sep 15 '11 at 8:00
I know, I was asking another question before but exited because I figured it out :) Thanks I'll give that a try – UVic Student Sep 15 '11 at 8:02
You can also use the formula for slope: $m=\Delta y / \Delta x$, plugging in $m=-2/3$ and $\Delta x = -12$. Does this sound familiar at all? – anon Sep 15 '11 at 8:07
Yes it does... I really should have known/thought of that, actually. Thank you! – UVic Student Sep 15 '11 at 8:09

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, $∆f(x) = -8$.

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OP asked the question over 3 months ago and is probably no longer interested in the answer, but math is eternal. – Gerry Myerson Dec 26 '11 at 4:14
Is it bad practice to answer old questions? I come across a lot of questions from the "related" sidebar that way, and I think others who might be interested in a similar question and would be glad to see a thorough response. – Samuel Reid Dec 26 '11 at 6:33
There's nothing wrong with answering old questions, provided you're aware (as you clearly were) that they are old questions and that the person who asked the question is unlikely to derive any benefit from your answer. – Gerry Myerson Dec 26 '11 at 15:58