Answer
Solve the equation for $y$, transforming it into the slope–intercept form $y=mx+b$. The coefficient of $x$ will be the slope of the line and the constant term will be the $y$ intercept.
Work Step by Step
Consider the general form of a line’s equation
$Ax+By+C=0$
Follow the steps given below to calculate the slope and y intercept of the given general equation:
Step 1: Find the value of $y$ by rearranging the terms of the equation
$Ax+By+C=0$
Subtract $Ax+C$ from both sides of the above equation:
$\begin{align}
& Ax+By+C-Ax-C=0-Ax-C \\
& By=-Ax-C
\end{align}$
Divide both sides by B
$\begin{align}
& \frac{By}{B}=\frac{-Ax-C}{B} \\
& y=-\frac{A}{B}x-\frac{C}{B}
\end{align}$
Step 2: Then compare it to the slope intercept form of the line.
The coefficient of $x$ will be the slope of the line and the constant term will be the $y$ intercept.
So, the slope of the line is $m=-\frac{A}{B}$ and the $y$ intercept is $b=-\frac{C}{B}$.
Example:
Consider the following line’s equation
$3x-4y-6=0$
Step 1: To find the value of $y$, rearrange the terms of the equation
Subtract $3x-6$ from both sides of the equation
$\begin{align}
& 3x-4y-6=0 \\
& 3x-4y-6-\left( 3x-6 \right)=0-\left( 3x-6 \right) \\
& 3x-4y-6-3x+6=0-3x+6 \\
& -4y=-3x+6
\end{align}$
Divide both sides by $-4$
$\begin{align}
& \frac{\left( -4y \right)}{\left( -4 \right)}=\frac{-3x+6}{\left( -4 \right)} \\
& y=\frac{3}{4}x-\frac{3}{2}
\end{align}$
Step 2: Compare it to the slope-intercept form of the line. The coefficient of $x$ will be the slope of the line and the constant term will be the $y$ intercept.
So, the slope of the line is $m=\frac{3}{4}$ and the $y$ intercept is $b=-\frac{3}{2}$.
