Question

How do you write \[y - 11 = 3(x - 2)\] in standard form.

Answer 1

Hint: The equation is an algebraic equation, where the algebraic equation is the combination of constants and variables. Here in this question we have to write the given equation in the form of standard form.

Complete step by step solution:
 The algebraic expression is an expression which consists of variables and is consistent with the arithmetic operations. The above equation is a linear equation where the linear equation is defined as the equations are of the first order. These equations are defined for lines in the coordinate system. To solve this linear equation, we apply simple methods.
The standard form for the linear equation is given as \[ax + by + c = 0\] and it is also defined as \[y = mx + c\] where m represents the slope of the line of equation.
Now consider the given equation
 \[y - 11 = 3(x - 2)\]
On multiplying in this RHS we get
 \[ \Rightarrow y - 11 = 3x - 6\]
Take -11 to the RHS and we get
 \[ \Rightarrow y = 3x - 6 + 11\]
On simplifying we get
 \[ \Rightarrow y = 3x + 5\]
This is the standard form.
The other form of the standard form of the equation
Now consider the given equation
 \[y - 11 = 3(x - 2)\]
On multiplying in this RHS we get
 \[ \Rightarrow y - 11 = 3x - 6\]
Take -11 to the RHS and we get
 \[ \Rightarrow y = 3x - 6 + 11\]
On simplifying we get
 \[ \Rightarrow y = 3x + 5\]
Take y to the RHS and we get
 \[ \Rightarrow 3x - y + 5 = 0\]
This is another form of standard form.
So, the correct answer is “3x - y + 5 = 0”.

Note: The algebraic equation or an expression is a combination of variables and constants, it also contains the coefficient. The alphabets are known as variables. The x, y, z etc., are called as variables. The numerals are known as constants. The numeral of a variable is known as co-efficient. We have 3 types of algebraic expressions namely monomial expression, binomial expression and polynomial expression. By using the tables of multiplication, we can solve the equation.