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In the equation $ y = ax + b $ which is the subject of the formula?
A. $ x $
B. $ y $
C. $ a $
D. $ b $

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Last updated date: 24th Feb 2024
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IVSAT 2024
Answer
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Hint: First of all we shall learn about the subject of formula. Generally, a formula is nothing but an equation that is expressed in variables and constants using mathematical operations. That is, a formula consists of variables and constants.
When we are asked to find the value of those variables using hints given in the equation, it can be called the subject of the formula. The subject of the formula can also be defined as the variable which depends on other variables.
 For example, let us consider the formula for the perimeter of a rectangle.
\[P = 2 \times l + 2 \times w\]
Where P is the perimeter of a rectangle, l is the length and w is the width of a rectangle.
Here, P is the subject of the formula since it depends on the variables l and w.
And our question is to find the subject of the formula for the given algebraic equation $ y = ax + b $ .

Complete step by step answer:
The algebraic equation is $ y = ax + b $ .
Here, there are four variables $ x $ , $ y $ , $ a $ , $ b $ .
The variable $ x $ does not depend on any other variable because it remains constant when there are changes in the variable. Hence, the variable $ x $ is not subject to the formula.
Similarly, the variables $ a $ and $ b $ are not subject to the formula.
Next, we shall check the variable $ y $ .
The variable $ y $ depends on the other variables $ x $ , $ a $ and $ b $ in the given equation $ y = ax + b $ .
Hence, the variable $ y $ is the subject of the formula for the given algebraic equation $ y = ax + b $ .

So, the correct answer is “Option B”.

Note: A formula consists of variables and constants. When we are asked to find the value of those variables using hints given in the equation, it can be called the subject of the formula. The subject of the formula can also be defined as the variable which depends on other variables.