Standard Form

1. Graph $12 x-9 y=36$.

2. Graph $3 x+4 y=12$.

3. Graph $x+3 y=6$.

4. Graph $-14 x+21 y=84$.

1. This is a linear equation given in standard form: $A x+B y=C$. A common way of graphing an equation of this form is to find the $x$- and $y$-intercepts of the graph.

To find the $y$-intercept, let's substitute $x=0$ into the equation and solve for $y$:

$\begin{aligned} 12 x-9 y &=36 \\ 12 \cdot 0-9 y &=36 \\ -9 y &=36 \\ y &=-4 \end{aligned}$

So the $y$-intercept is $(0,-4)$.

To find the $x$-intercept, let's $y=0$ into the equation and solve for $x$:

$\begin{aligned} 12 x-9 y &=36 \\ 12 x-9 \cdot 0 &=36 \\ 12 x &=36 \\ x &=3 \end{aligned}$

So the $x$-intercept is $(3,0)$.

We can graph the linear equation using these two points, as shown below:

2. This is a linear equation given in standard form: $A x+B y=C$. A common way of graphing an equation of this form is to find the $x$- and $y$-intercepts of the graph.

To find the $y$-intercept, let's substitute $x=0$ into the equation and solve for $y$:

$\begin{array}{r} 3 x+4 y=12 \\ 3 \cdot 0+4 y=12 \\ 4 y=12 \\ y=3 \end{array}$

So the $y$-intercept is $(0,3)$.

To find the $x$-intercept, let's $y=0$ into the equation and solve for $x$:

$\begin{array}{r} 3 x+4 y=12 \\ 3 x+4 \cdot 0=12 \\ 3 x=12 \\ x=4 \end{array}$

So the $x$-intercept is $(4,0)$.

We can graph the linear equation using these two points, as shown below:

3. This is a linear equation given in standard form: $A x+B y=C$. A common way of graphing an equation of this form is to find the $x$- and $y$-intercepts of the graph.

To find the $y$-intercept, let's substitute $x=0$ into the equation and solve for $y$:

$\begin{array}{r} x+3 y=6 \\ 0+3 y=6 \\ 3 y=6 \\ y=2 \end{array}$

So the $y$-intercept is $(0,2)$.

To find the $x$-intercept, let's $y=0$ into the equation and solve for $x$:

$\begin{array}{r} x+3 y=6 \\ x+3 \cdot 0=6 \\ x=6 \end{array}$

So the $x$-intercept is $(6,0)$.

We can graph the linear equation using these two points, as shown below:

4. This is a linear equation given in standard form: $A x+B y=C$. A common way of graphing an equation of this form is to find the $x$- and $y$-intercepts of the graph.

To find the $y$-intercept, let's substitute $x=0$ into the equation and solve for $y$:

$\begin{aligned} -14 x+21 y &=84 \\ -14 \cdot 0+21 y &=84 \\ 21 y &=84 \\ y &=4 \end{aligned}$

So the $y$-intercept is $(0,4)$.

To find the $x$-intercept, let's $y=0$ into the equation and solve for $x$:

$\begin{array}{r} -14 x+21 y=84 \\ -14 x+21 \cdot 0=84 \\ -14 x=84 \\ x=-6 \end{array}$

So the $x$-intercept is $(-6,0)$.

We can graph the linear equation using these two points, as shown below:

1. What is $y-8=3(x+1)$ written in standard form?

Choose 1 answer:

A. $y-8=3 x+3$

B. $y=3 x+11$

C. $-3 x+y-11=0$

D. $-3 x+y=11$

2. What is $y=\frac{4}{5} x+2$ written in standard form?

Choose 1 answer:

A. $-\frac{4}{5} x+y-2=0$

B. $y=\frac{4}{5}\left(x+\frac{5}{2}\right)$

C. $5 y=4 x+10$

D. $-4 x+5 y=10$

3. What is $y+5=7(x-8)$ written in standard form?

Choose 1 answer:

A. $x-7 y=-61$

B. $7 x+y=-61$

C. $-7 x+y=-61$

D. $x+7 y=-61$

4. What is $y=-\frac{3}{10} x-8$ written in standard form?

Choose 1 answer:

A. $10 x+3 y=-80$

B. $10 x-3 y=-80$

C. $-3 x+10 y=-80$

D. $3 x+10 y=-80$

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.

$y-8=3(x+1)$ 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.

$y=\frac{4}{5} x+2$ 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.

$y+5=7(x-8)$ 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.

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