Standard Form

When a linear equation is written in standard form, both variables x and y are on the same side of the equation. Watch this lecture series and practice converting equations to 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 $3 x+10 y=-80$ .