# What is the math equation that satisfies conditions given below?

Variable $z$ varies from $-50.0$ to $18.0$. Find the equation that gives $d$ such that when $z=-50$, $d = 0.1$; and when $z = 18.0$, $d = 1.0$. The values of $d$ vary from 0.1 to 1 uniformly depending on the value of $z$ with the boundary conditions given above.

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Let $d = az + b$. Solve two equations in two variables. – Yuval Filmus Feb 22 '11 at 17:28
Is this homework? Try finding the slope of the line going through the two points $(-50,0.1)$ and $(18,1)$, and then working out what the $y$-intercept has to be. – Zev Chonoles Feb 22 '11 at 17:33
No this is not homework. Just writing some program. So how do I find constants and a and b if the equation looks like d = az+b ? Is there mathematical way to find these constants? – user7378 Feb 22 '11 at 17:54

As $d$ changes from $0.1$ to $1$ (a change of $1-0.1=0.9$), $z$ changes from $-50$ to $18$ (a change of $18--50=68$), so for every change of $1$ in $z$, $d$ changes by $\frac{0.9}{68}$. When $z=-50$, $d=0.1$. So, an equation relating $z$ and $d$ is $$d-0.1=\frac{0.9}{68}(z+50).$$