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How do you notate the insertion of values in a formerly defined formula? When you have the $x,y$-tupel $(a1;b1)$ and following text:

$$f(x)=mx+b \tag{1.1}$$

$$b_1=ma_1+b$$

Is there a math sign to denote "usage"?

user87690
  • 9,133
Jan
  • 153

1 Answers1

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First, if you want to use an object later, you have to give it a name.

Second, you cannot insert two values into $f(x) = mx + b$ since it has only one variable. If it is the definition of $f$, then you already have a name, and you han write $f(a_1)$, which is equal to $ma_1 + b$, and you can ask whether it equals $b_1$. On the other hand, if it is just an equation, then you can name it for example like this: $R(x): f(x) = mx + b$. Then you can insert a value into it: $R(a_1): f(a_1) = ma_1 + b$.

If you want equation with two variables, you have to write it like that: $R(x, y): y = mx + b$. Then you can insert the pair: $R(a_1, b_1): b_1 = ma_1 + b$.

user87690
  • 9,133