Convert linear equations to standard form - Questions

Answers

1. D. \(-3 x+y=11\)

Standard linear equations are in the general form \(A x+B y=C\) where \(A\), \(B\), and \(C\) are constants.

Usually, \(A\), \(B\), and \(C\) are integers.

\(y-8=3(x+1)\)
\(y-8=3 x+3\) Distribute.
\(y=3 x+11\) Collect constants.
\(-3 x+y=11\) Bring to standard form.

\(y-8=3(x+1)\) written in standard form is \(-3 x+y=11\).


2. D. \(-4 x+5 y=10\)

Standard linear equations are in the general form \(A x+B y=C\) where \(A\), \(B\), and \(C\) are constants.

Usually, \(A\), \(B\), and \(C\) are integers.

\(y=\frac{4}{5} x+2\)
\(5 y=4 x+10\) Multiply by denominator.
\(-4 x+5 y=10\) Bring to standard form.


\(y=\frac{4}{5} x+2\) written in standard form is \(-4 x+5 y=10\).


3. C. \(-7 x+y=-61\)

Standard linear equations are in the general form \(A x+B y=C\) where \(A\), \(B\), and \(C\) are constants.

Usually, \(A\), \(B\), and \(C\) are integers.

\(y+5=7(x-8)\)
\( y+5=7 x-56\) Distribute.
\(y=7 x-61\) Collect constants.
\(-7 x+y=-61\) Bring to standard form.


\(y+5=7(x-8)\) written in standard form is \(-7 x+y=-61\).


4. D. \(3 x+10 y=-80\)

Standard linear equations are in the general form \(A x+B y=C\) where \(A\), \(B\), and \(C\) are constants.

Usually, \(A\), \(B\), and \(C\) are integers.

\(y=-\frac{3}{10} x-8\)
\(10 y=-3 x-80\) Multiply by denominator.
\(3 x+10 y=-80\) Bring to standard form.


\(y=-\frac{3}{10} x-8\) written in standard form is \(3 x+10 y=-80\).