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Question: How do you write \(y=\dfrac{-2}{5}x+\dfrac{1}{10}\) in standard form?...

How do you write y=−25x+110y=\dfrac{-2}{5}x+\dfrac{1}{10} in standard form?

Explanation

Solution

We are given y=−25x+110y=\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=0ax+by+c=0. So, we reduce it to this form.

Complete step by step answer:
We are given that y=−25x+110y=\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=−25x+110y=\dfrac{-2}{5}x+\dfrac{1}{10} has 22 variables x and y, both of these variables has power 11, 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=−25x+110y=\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=0ax+by+c=0
Where a,b,c are integers.
So, we have to change y=−25x+110y=\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=−25x+110y=\dfrac{-2}{5}x+\dfrac{1}{10}
So as we see that denominator of value on the right hand side is 5 and 105\,\text{and}\,10.
So we multiply both side by 1010
We get
10×y=10(−25x+110)10\times y=10\left( \dfrac{-2}{5}x+\dfrac{1}{10} \right)
Simplifying we get
10y=−4x+110y=-4x+1
Now we add 4x4x on both sides.
4x+10y=4x−4x+14x+10y=4x-4x+1
So we get
4x+10y=0+14x+10y=0+1 [as −4x+4x=0]\left[ \text{as}\,-4x+4x=0 \right]
Now we subtract 11 from both sides
4x+10y−1=1−14x+10y-1=1-1
Simplify we get
4x+10y−1=0       [as 1−1=0]4x+10y-1=0\,\,\,\,\,\,\,\left[ \text{as}\,1-1=0 \right]
So, we get
y=−25x+110y=\dfrac{-2}{5}x+\dfrac{1}{10}
4x+10y−1=04x+10y-1=0

Standard form of y=−25x+110y=\dfrac{-2}{5}x+\dfrac{1}{10} is 4x+10y−1=04x+10y-1=0

Note: While multiplying, remember that is term has more than 11 term then we multiply term by all terms i.e. a(b+c)=a×b+a×ca(b+c)=a\times b+a\times c do not do error like a(b+c)=ab+ca(b+c)=ab+c
Similarly when we subtract things we need to be very accurate, always like 2−(−2)=42-(-2)=4. Do not make errors like 2−(−2)=02-(-2)=0.
It is first simplified as 2−(−2)=2+22-(-2)=2+2 then we get 44 as an answer.