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I am stumped on this problem. On the surface, this seems like this should be relatively easy, middle school algebra. I cannot seem to come to a final equation that will work for my task at hand.

Given an X-coordinate value, what is the corresponding Y-coordinate value on the line? For example: I know the X value of 97.75%. How can I use an equation to come up with the Y-value that falls on the line, in the case of X=97.75% Y=25.

I have tried to come up with a formula for the line. When I try to solve for the slope of the first graph, I get 33.33. This doesn't seem correct to me. The graphs are from Excel. Within Excel I can click on the line, click "add trend line", and then click show equation. The equation that is displayed is Y= -25x + 125. When I plug in, for example, 97.75 and solve for Y I am left with a large negative number.

I feel like I am forgetting/missing some fundamentals here. Any help is appreciated. Again the goal is to come up with an equation so I can solve for the Y-coordinate value. "Given a percentage (X-axis), tell me the score (Y-axis)".

Graph 1:
(97%, 0), (97.75%, 25), (98.50%, 50), (99.25%, 75), (100%, 100)

Graph 2: (80%, 0), (85%, 25), (90%, 50), (95%, 75), (100, 100)

Graphs

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The slope of the first line is $\frac{100}{3}$, because you can take the points $(97, 0)$ and $(100, 100)$, then calculate the slope as $$\frac{y_2-y_1}{x_2-x_1} = \frac{100 - 0}{100 - 97} = \frac{100}{3}.$$

How you managed to get the formula $-25x + 125$ from excel is beyond me, but it is probably not a mistake in Excel, but a mistake in your use of it. However, for help with Excel, this is not the correct site.

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  • $\begingroup$ Thanks for the response, however I was not asking for help with Excel. As for 100/3 as the slope, as stated in my post, I did arrive to this value as well. If this is indeed the slope of the line, how can I solve for the Y-value on the line, given X and this slope? $\endgroup$ – mathfan99 Oct 26 '15 at 16:12
  • $\begingroup$ @mathfan99 I know, I am just telling you that the mistake you made was not a mathematical one. The $33.33$ you calculated is correct. $\endgroup$ – 5xum Oct 26 '15 at 16:13
  • $\begingroup$ If 33.33 is the slope, given 97.75 as X-coordinate how do you calculate 25 as the y coordinate? This is what I am having trouble coming up with an equation for, if its possible. $\endgroup$ – mathfan99 Oct 26 '15 at 16:25
  • $\begingroup$ @mathfan99 Well, you need more than just the slope. You need to calculate both $k$ and $n$ in the equation $y=kx + n$. $\endgroup$ – 5xum Oct 26 '15 at 16:37

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