Question

How do you write the equation \[y-2=\dfrac{-2}{5}\left( x-8 \right)\] in standard form?

Answer 1

Hint: In this question we have to convert the given linear equation having two variables into standard form. The standard form for linear equations in two variables is \[Ax+By=c\]. So we have remove the fraction by multiplying it with its inverse and after that we will rearrange the terms on the left hand side so the equal to sign and equal it with constant term, which means that constant term must be on right hand side of the equal to sign, after doing this we will get our required answer.

Complete Step by Step solution:
We have given linear equation in two variable is as follows:-
\[y-2=\dfrac{-2}{5}\left( x-8 \right)..............(i)\]
In order to convert it in a standard form for linear equations in two variables we will compare equation \[\left( i \right)\]with \[Ax+By=c\].
on multiplying both sides by \[5\]we get, \[5\left( y-2 \right)=-2\left( x-8 \right)\]
\[\Rightarrow 5y-10=-2x+16\]
\[\Rightarrow 5y+2x=16+10\]
\[\Rightarrow 5y+2x=26\] Which is standard form for given linear equation in two variable \[y-2=\dfrac{-2}{5}\left( x-8 \right)\]

Note:
“An equation is said to be linear equation in two variable if it is written in the form of \[ax+bx=c\] where \[a,b\]and \[c\] are real numbers and the coefficients of \[x\]and \[y\]that is \[a\]and \[b\]respectively are not equal to zero.