How do you write $4y - 8x + 12 = 0$ in slope-intercept form?

Hint: The equation of a straight line in slope-intercept form is: $y = mx + b$. Where m is the value of slope and b is the y-intercept. Here, m and b are constants, and x and y are variables. In this question, a linear equation is given. We will convert this equation into the form of a straight-line equation. By comparing with the standard equation we will find the value of slope and the value of intercept.

Complete step-by-step solution:
In this question, the linear equation is
$ \Rightarrow 4y - 8x + 12 = 0$
Let us subtract 12 on both sides.
$ \Rightarrow 4y - 8x + 12 - 12 = 0 - 12$
That is equal to,
$ \Rightarrow 4y - 8x = - 12$
Now, let us add 8x on both sides.
$ \Rightarrow 4y - 8x + 8x = - 12 + 8x$
That is equal to,
$ \Rightarrow 4y = 8x - 12$
Now, let us divide both sides by 4.
$ \Rightarrow \dfrac{{4y}}{4} = \dfrac{{8x - 12}}{4}$
Split the denominator on the right-hand side.
$ \Rightarrow y = \dfrac{{8x}}{4} - \dfrac{{12}}{4}$
Let us simplify the right-hand side. The division of 8 and 4 is 2, and the division of 12 and 4 is 3.
Therefore,
$ \Rightarrow y = 2x - 3$
The above equation is in the standard form of the straight-line.
Now, let us compare the above equation with $y = mx + b$.
Here, the value of $m$ is $2$ and the value of $b$ is $-3.$

Hence, the value of the slope is 2 and the value of the y-intercept is -3.

Note: In the straight-line equation, x and y are variables that describe the position of specific points on the graph, m and b describe features of the function. A straight line is a linear equation of the first order. The slope is a horizontal line then the value of y is always the same. The slope is a vertical line then the value of x is always the same.