Question

How do you write $y - 10 = 2\left( {x - 8} \right)$?

Answer 1

Hint: In this question we have to write the given equation in the standard form, we know that the standard form of the linear equation is given by $Ax + By = C$ where, if at all possible, A, B, and C are integers, and A is non-negative, and, A, B, and C have no common factors other than 1, we will first simplify the equation and substitute the values in the form we will get the required result.

Complete step by step solution:
The Standard Form for a linear equation in two variables,$x$ and $y$, is usually given as $Ax + By = C$ where, if at all possible, A, B, and C are integers, and A is non-negative, and, A, B, and C have no common factors other than 1.
Given equation is $y - 10 = 2\left( {x - 8} \right)$,
Now simplifying the equation we get,
$ \Rightarrow y - 10 = 2x - 16$,
Rewrite the given equation by subtracting both sides $y$we get,
$ \Rightarrow y - 10 - y = 2x - y - 16$,
Now simplifying we get,
$ \Rightarrow - 10 = 2x - y - 16$,
Now add 16 to both sides we get,
$ \Rightarrow - 10 + 16 = 2x - y - 16 + 16$,
Now simplifying we get,
$ \Rightarrow 6 = 2x - y$,
Now rewriting the equation we get,
$ \Rightarrow 2x - y = 6$,
And we know that standard form for a linear equation in two variables, $x$ and $y$, is given as $Ax + By = C$,
So, here $A = 2$,$B = - 1$and $C = 6$,
So, the standard form of the given equation is $2x - y = 6$.

$\therefore $ The standard form of the given equation $y - 10 = 2\left( {x - 8} \right)$ will be equal to $2x - y = 6$.

Note: Linear equations represent a straight line. Linear equations in two variables make it easy to explain the geometry of lines or the graph of two lines or equations, it contains two variables whose values are unknown. The linear equations of two variables can be solved by converting the situation into mathematical statements which tell the relation between the unknown variables and it makes it easier to solve such problems.