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I'm trying to figure out the formula of X to Y based on the following two examples:

If $X = 78.6$ then $Y = 3.8 \%$

If $X = 72.9$ then $Y = 4.3\%$

As X decreases Y raises. I'd like to be able to calculate:

What is $X$ if $Y = 15\%$ ?

What is $X$ if $Y = 12\%$ ?

What is $X$ if $Y = 10\%$ ?

callculus42
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user1444027
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1 Answers1

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To find some line $ax+b$ that fits the two data points you solve the system $$ 78.6a + b = 3.8\\ 72.9a+b = 4.3 $$ which gives $$ a \approx -\frac{1}{11.4}, \quad b \approx 10.7 $$ So you have the line $$ y = -\frac{1}{11.4}x + 10.7 $$ So for example to find $x$ such that $y=10$ you just plug in for $y$ $$ 10 = -\frac{1}{11.4}x + 10.7 $$ and solve for $x$ to get $$ x = 7.98 $$