The standard form of a line is $\displaystyle \small Ax+By=C$, where all constants are integers, i.e. whole numbers.

Therefore, the equation written in standard form is $\displaystyle \small 2x+4y=7$.

First, we need to find the slope of the above line. 

Given two points, $\displaystyle (x_{1}, y_{1}), (x_{2}, y_{2})$, the slope can be calculated using the following formula:

$\displaystyle m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $\displaystyle x_{1}=-4, y_{1}=x_{2}= 0, y_{2}=8$:

$\displaystyle m = \frac{8-0}{0-(-4)} = \frac{8}{4} = 2$

Second, we note that the $\displaystyle y$-intercept is the point $\displaystyle (0,8)$. 

Therefore, in the slope-intercept form of a line, we can set $\displaystyle m = 2$ and $\displaystyle b = 8$:

$\displaystyle y = mx+b$

$\displaystyle y = 2x+8$

Since we are looking for standard form - that is, $\displaystyle Ax+By = C$ - we do the following:

$\displaystyle y - y - 8 = 2x+8 - y - 8$

$\displaystyle -8 = 2x -y$

or 

$\displaystyle 2x - y = -8$

Standard form of an equation is

$\displaystyle Ax+By=C$.

Rearrange the given equation to make it look like the above equation as follows:

$\displaystyle y=-3x+2$

$\displaystyle y+3x=-3x+3x+2$

$\displaystyle y+3x=2$

$\displaystyle 3x+y=2$

The standard form of a line is $\displaystyle Ax+By=C$, where $\displaystyle A, B, \textup{and}\textup{ } C$ are integers. 

We therefore need to rewrite $\displaystyle 2+4y=3x+10$ so it looks like $\displaystyle Ax+By=C$.

The steps to do this are below:

$\displaystyle 2+4y=3x+10 \textup{ (subtract 10 from both sides)}$

$\displaystyle -8 +4y=3x\textup{ (subtract 4y from both sides)}$

 $\displaystyle -8=3x-4y\ (\textup{flip the two sides of the equality})$

$\displaystyle 3x-4y=-8$

To rewrite in standard form, we will need the equation in the form of:

$\displaystyle Ax+By =C$

Subtract $\displaystyle 3x$ on both sides.

$\displaystyle y-3x=3x+8-3x$

Regroup the variables on the left, and simplify the right.

The answer is:  $\displaystyle -3x+y =8$

The given equation is in point-slope form.

The standard form is:  $\displaystyle Ax+By = C$

Distribute the right side.

$\displaystyle y-2=3x+18$

Subtract $\displaystyle 3x$ on both sides.

$\displaystyle y-2-3x=3x+18-3x$

$\displaystyle -3x+y-2 = 18$

Add 2 on both sides.

$\displaystyle -3x+y-2+2 = 18+2$

The answer is:  $\displaystyle -3x+y = 20$

The standard form of a linear equation is:  $\displaystyle Ax+By =C$

Reorganize the terms.

Add $\displaystyle 9x$ on both sides.

$\displaystyle 3+y-9x+(9x)=4+(9x)$

$\displaystyle 3+y= 4+9x$

Subtract $\displaystyle y$ on both sides.

$\displaystyle 3+y-y= 4+9x-y$

$\displaystyle 3= 4+9x-y$

Subtract four on both sides.

$\displaystyle 3-4= 4+9x-y-4$

The answer is:  $\displaystyle 9x-y = -1$

Write the slope-intercept form of a linear equation.

$\displaystyle y=mx+b$

Substitute the point and the slope.

$\displaystyle -3 = (2)(4)+b$

Solve for the y-intercept, and then write the equation of the line.

$\displaystyle -3 = 8+b$

$\displaystyle -3-8 = 8+b-8$

$\displaystyle b=-11$

$\displaystyle y=2x-11$

The equation in standard form is:  $\displaystyle Ax+By =C$

Subtract $\displaystyle 2x$ from both sides.

$\displaystyle y-2x=2x-11-2x$

The answer is:  $\displaystyle -2x+y = -11$

The equation in standard form of a linear equation is:  

$\displaystyle Ax+By =C$

The equation in standard form of a parabolic equation is:  

$\displaystyle y= Ax^2+Bx+C$

All of the following equations are in standard form except:

$\displaystyle y-2=3(x+9)$

This equation is in point-slope format:  $\displaystyle y-y_1 = m(x-x_1)$

The answer is:  $\displaystyle y-2=3(x+9)$

The standard form of a linear equation is:  $\displaystyle Ax+By =C$

Distribute the right side.

$\displaystyle y-2 = 3x-9$

Subtract $\displaystyle 3x$ on both sides.

$\displaystyle y-2 -(3x)= 3x-9-(3x)$

$\displaystyle -3x+y-2 = -9$

Add 2 on both sides.

$\displaystyle -3x+y-2+2 = -9+2$

The answer is:  $\displaystyle -3x+y = -7$