What is $3x-4y=12$ in slope – intercept form?

Hint: To convert the given linear equation of a line in the slope intercept form, leave the term containing the variable y in the L.H.S and take all other terms to the R.H.S. Now, make the coefficient of y equal to 1 by dividing both the sides with -4 and simplify. Compare the obtained linear equation with the slope-intercept form of a line given as \[y=mx+c\]. Here, ‘m’ is the slope of the line and ‘c’ is its y- intercept.

Complete step-by-step solution:
Here we have been provided with the linear equation $3x-4y=12$ and we have been asked to write it in the slope intercept form. Let us first we know about the slope – intercept form of a linear equation.
Now, the given equation of the line $3x-4y=12$ is of the form $Ax+By+C=0$, where A, B and C are constants. This representation of a linear equation is known as the standard form of a line. In slope-intercept form we write the equation of a line as \[y=mx+c\], where ‘m’ represents the slope and ‘c’ represents the intercept on y- axis. So we need to send all the variables except y to the R.H.S and make the coefficient of y equal to 1. Therefore we have,
$\begin{align}
  & \Rightarrow 3x-4y=12 \\
 & \Rightarrow -4y=-3x+12 \\
\end{align}$
Dividing both the sides of the equation with -4 we get,
$\begin{align}
  & \Rightarrow y=\dfrac{-1}{4}\left( -3x+12 \right) \\
 & \therefore y=\dfrac{3}{4}x-3 \\
\end{align}$
Hence, the above linear equation represents the slope-intercept form of the line.

Note: Note that if you wish to find the values of slope and y-intercept then you may compare the obtained expression with \[y=mx+c\]. In the standard form of the line $Ax+By+C=0$, slope is given as \[\dfrac{-B}{A}\] and the y- intercept for this form is given as \[\dfrac{-C}{A}\]. In the intercept form we write the equation as $\dfrac{x}{a}+\dfrac{y}{b}=1$ where ‘a’ and ‘b’ are the x-intercept and y-intercept respectively.