Question

How can you solve for $b$ in $y = mx + b$ ?

Answer 1

Hint: The equation $y = mx + b$ is nothing but the linear equation. The equation $y = mx + b$ for a straight line, the $m$ is nothing but the slope of the line and the $b$ is called the y-intercept of the line. In order to solve for $b$ just simplify the given equation.

Complete step by step answer:
In the given question the equation $y = mx + b$ is nothing but the linear equation, from which they have asked to solve for$b$ . In order to solve for $b$ first we need to know what is $x$, $y$ , $m$ and $b$ in the given equation $y = mx + b$ .
Given, $y = mx + b$
Where, $x,y$ are coordinates
              $m$ is the slope and
             $b$ is the y-intercept.
Now in order to solve for $b$ in the given equation $y = mx + b$ we make some necessary changes, so that we can arrive at the required answer.
Now, for the given linear equation $y = mx + b$ , subtract the $mx$ on both the left hand side and the right hand side, just to make the simplification easier.
Therefore, we get
$ \Rightarrow y - mx = mx + b - mx$
In the above equation, we can see that in the right hand side equation the term $mx$ gets cancelled. So we can write as
$ \Rightarrow y - mx = b$ Which is the equation for $b$ which they have asked in the question.
Hence, $b = y - mx$ .

Note: Whenever we have this type of question, where we have an expression $y = mx + b$ and asked to solve for $b$ which is present in the given expression. We just have to simplify the expression $y = mx + b$ in such a way that we get the correct answer or the expression for $b$ . In this problem you need to be careful while simplifying the expression as it will be the major part.