Question

How do you write the equation \[y + 9 = - 3(x - 2)\] in standard form?

Answer 1

Hint: In this question, we are given an equation and we have been asked to convert it into the standard form. The standard form of the equation is \[Ax + By = C\] . We can simply shift all the variable terms to the left-hand side and all the constants to the right-hand side. Then, we will add or subtract the required terms and also make sure that coefficient of x is positive. If it is not, make it positive. You will get the required standard form of the equation.

Formula used: Any linear equation can be written as two following way:
\[1.\] Slope-intercept form of a linear equation.
\[2.\] Standard form of a linear equation.
Most of the time, any linear equation is written in slope-intercept form.
\[1.\] The general equation of slope-intercept form is as following:
\[y = m.x + c\] , where \[y,x\] are variables of the equation and \[c\] is the constant term.
And, \[m\] is called the slope of the line.
\[m\] can have positive value or negative value, or it can be any fractional value or any real number.
So, the slope tells the character of any straight line.
\[2.\] The general form of standard form is as following:
\[Ax + By = c\].
But the above form shall follow the following points:
 \[I.\] ‘\[A\]’ must be a positive number, it cannot be a negative number.
\[II.\] \[A,B\] and \[C\] must be integers, they cannot be fractional numbers.

Complete step-by-step solution:
It is given in the question that:
\[y + 9 = - 3(x - 2)\].
Now, multiply the terms in R.H.S, we get:
$\Rightarrow$\[y + 9 = - 3x + 6\].
Now, taking all the variables to the L.H.S, we get:
$\Rightarrow$\[y + 3x = - 9 + 6.\]
Now, by doing the further simplification, we get:
$\Rightarrow$\[3x + y = - 3.\]
So, by comparing the above standard form of equation, we can say that the term \[A = 3\] , which is positive, and \[B = 1\] , \[C = - 3\] , which are integers too.

\[\therefore \]The standard form of the given equation is \[3x + y = - 3.\]

Note: We need to simplify any linear equation to get the variables and constant terms on the different sides of the equation.
Slope of any linear equation tells us the character of the equation and the standard form of an equation helps us the number of integral solutions that exist for the equation.
When the variables in a linear equation are easy to interpret, that form of the equation is called a standard form.
We need to put one aside of the equation and the constant terms are into another side so that it is easy to define the coefficients associated with the variables.