Question

Rearrange the formula to make $w$ the subject $5w - 3y + 7 = 0$

Answer 1

Hint: We will first understand what does the question means by making the subject, then we will just rearrange the terms by keeping $w$ on the LHS and the rest of all the terms on RHS to get the required answer.

Complete step by step answer:
We are given that we need to make $w$ as the subject of our equation.
Making something a subject of anything basically refers to making the equation such that, we find the values of w whenever we put in any values of $y$. So, in simpler words, we need to find the function w in terms of $y$.
So, for doing that, we just need to rearrange the terms by keeping w on the LHS and rest everything on RHS.
First of all, we will take the $7$ from addition in LHS to subtraction in RHS, then we will get:-
$ \Rightarrow 5w - 3y = 0 - 7$
Simplifying the RHS to obtain the following expression:-
$ \Rightarrow 5w - 3y = - 7$
Now, we will take the 3y from subtraction in LHS to addition in RHS to get the following expression
$ \Rightarrow 5w = 3y - 7$
Now, we will take the 7 from multiplication in LHS to division in RHS, we will get
$ \Rightarrow w = \dfrac{{3y - 7}}{5}$.
Hence, we have thus rearranged the equation to make $w$ as a subject of it.

Hence, the required answer is $w = \dfrac{{3y - 7}}{5}$.

Note:
The students must note that this is the equation of a line which we are dealing with. If you have any equation with two variables with a degree being 1, you will always get a line.
We can $5w - 3y + 7 = 0$ as a linear equation in w and y. If we compare $w = \dfrac{{3y - 7}}{5}$ to $w = my + b$, where m is the slope of the line and b is the intercept. Then we will get the slope as $\dfrac{3}{5}$ and the intercept as $ - \dfrac{7}{5}$. We see that making a subject is helpful when we require to find the values of that particular variable. Like here, we can put in given values of $y$ to get the values of w.