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How do you write \[y=-\dfrac{2}{3}x+1\] in standard form?

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Last updated date: 26th Feb 2024
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IVSAT 2024
Answer
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Hint: According to the question we have to find the standard form of the given linear equation which is \[y=-\dfrac{2}{3}x+1\]. The standard form of an equation which is specifically a linear equation is \[ax+by=c\]. So here in solving the given question we will transform the given equation by doing some mathematical calculations and make it comparable with the standard form of linear equation.

Complete step-by-step solution:
Generally the standard form of the linear equation as we mentioned before will look like
\[ax+by=c\]. Here the x must be a non negative integer. So we will simplify the given equation by bringing the variables one side that is the left hand side and keep the constant 1 to the right hand side. After doing the equation will be as follows.
\[\Rightarrow y=-\dfrac{2}{3}x+1\]
\[\Rightarrow \dfrac{2}{3}x+y=1\]
Here after bringing the variables to one side of the equation we will make it compare to the standard form of the linear equation and it will look like as follows.
\[\Rightarrow \left( \dfrac{2}{3} \right)x+\left( 1 \right)y=1\]
Here the above equation is the standard form the given question \[\Rightarrow y=-\dfrac{2}{3}x+1\] and we can further simplify the equation into another form so that it looks without fractions by multiplying with 3 on both sides of the equation. After doing the above mentioned process the equation we will be transformed as follows.
\[\Rightarrow 2x+3y=3\]

Note: We must be very careful in doing the calculation and the students who are doing these questions must be having knowledge in the basic concept of linear equations and its applications. People cannot use the standard equation of the quadratic or other higher degree equations in solving these kinds of questions. We must also not leave it as \[\Rightarrow \left( \dfrac{2}{3} \right)x+\left( 1 \right)y=1\] after bringing the variable terms to left hand side we have to transform it into \[\Rightarrow 2x+3y=3\] which is the exact standard form.