Standard Form
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 \(3 x+10 y=-80\).