Question

What is the slope of the line represented by the equation \[2y=x-4\]?

Answer 1

Hint: Firstly, we will be considering the general line equation \[y=mx+c\] in which \[m\] is the slope of the line equation and \[c\] is the \[y-\text{intercept}\] of the line equation. So we will be solving our given equation and then converting it to the form of the general line equation will be giving us the slope of the line equation.

Complete step by step solution:
Now let us learn about the line equations. The general line equation is of the form \[y=mx+c\] where, \[m\] is the slope and \[c\] is the \[y\]\[-\] intercept. There are three major forms of line equations. They are: point-slope form, standard from and slope-intercept form.
Now let us find out the slope of the given equation of line.
We have the equation, \[2y=x-4\]
Firstly, we will be solving it for \[y\].
We get,
\[\begin{align}
  & \Rightarrow 2y=x-4 \\
 & y=\dfrac{x-4}{2} \\
\end{align}\]
Now upon splitting the terms separately, we get
\[\begin{align}
  & y=\dfrac{1}{2}x-\dfrac{4}{2} \\
 & y=\dfrac{1}{2}x-2 \\
\end{align}\]
Now we have the equation in the form of general equation i.e. \[y=mx+c\]
We have, \[m=\dfrac{1}{2}\] and \[c=2\].
As \[m\] represents slope, we have obtained the slope of the given equation.
\[\therefore \] The slope of the given equation \[2y=x-4\] as \[\dfrac{1}{2}\].

Note: For a non vertical line, if it passes through \[\left( x_0,y_0 \right)\] with the slope \[m\], then the equation of line would be \[y-y_0=m\left( x-x_0 \right)\]. The parallel lines will have equal slope. The slopes of the perpendicular lines are opposite reciprocals. When we have a line equation and we know the slope and \[y-\text{intercept}\] then we will be using the point-intercept method as shown above.
Now we will be plotting our given equation.