Question

How do you write $y=\dfrac{-2}{5}x+\dfrac{1}{10}$ in standard form?

Answer 1

Hint: We are given $y=\dfrac{-2}{5}x+\dfrac{1}{10}$. We are asked to find its standard form. To answer this we will first learn what type of equation we are handling once we learn that we focus on how to write the standard form of that particular form of equation then using the algebraic operation or tool we will simplify and reduce the given equation to the standard form. Whose standard form is given as \[ax+by+c=0\]. So, we reduce it to this form.

Complete step by step answer:
We are given that $y=\dfrac{-2}{5}x+\dfrac{1}{10}$, we are asked to write this equation in the standard form. To solve this problem, we will learn what is the standard form of the above equation.
Now we can see that given equation $y=\dfrac{-2}{5}x+\dfrac{1}{10}$ has \[2\] variables x and y, both of these variables has power \[1\], so they are linear means. We are given a linear equation In two variables.
We have to write the given linear equation in two variables $y=\dfrac{-2}{5}x+\dfrac{1}{10}$ into standard form.
We know that standard form for linear equation in two variables is given as \[ax+by+c=0\]
Where a,b,c are integers.
So, we have to change $y=\dfrac{-2}{5}x+\dfrac{1}{10}$
We will use algebraic tools like, addition, division, multiplication and subtraction to get to our solution.
As we have $y=\dfrac{-2}{5}x+\dfrac{1}{10}$
So as we see that denominator of value on the right hand side is \[5\,\text{and}\,10\].
So we multiply both side by \[10\]
We get
\[10\times y=10\left( \dfrac{-2}{5}x+\dfrac{1}{10} \right)\]
Simplifying we get
\[10y=-4x+1\]
Now we add \[4x\] on both sides.
\[4x+10y=4x-4x+1\]
So we get
\[4x+10y=0+1\] \[\left[ \text{as}\,-4x+4x=0 \right]\]
Now we subtract \[1\] from both sides
\[4x+10y-1=1-1\]
Simplify we get
\[4x+10y-1=0\,\,\,\,\,\,\,\left[ \text{as}\,1-1=0 \right]\]
So, we get
$y=\dfrac{-2}{5}x+\dfrac{1}{10}$
\[4x+10y-1=0\]

Standard form of $y=\dfrac{-2}{5}x+\dfrac{1}{10}$ is \[4x+10y-1=0\]

Note: While multiplying, remember that is term has more than \[1\] term then we multiply term by all terms i.e. \[a(b+c)=a\times b+a\times c\] do not do error like \[a(b+c)=ab+c\]
Similarly when we subtract things we need to be very accurate, always like \[2-(-2)=4\]. Do not make errors like \[2-(-2)=0\].
It is first simplified as \[2-(-2)=2+2\] then we get \[4\] as an answer.