So, we want to determine whether the lines:
[tex]\begin{gathered} y=\frac{1}{3}x+4 \\ x-3y=-12 \end{gathered}[/tex]First, remember that there are two different ways to represent a line with an equation. These are:
[tex]y=mx+b[/tex]Where m is the slope.
For example:
[tex]y=\frac{1}{3}x+4[/tex]Where the slope is 1/3.
The second way, has the equation of the form:
[tex]Ax+By+C=0[/tex]Where the slope is given by the operation:
[tex]\frac{-A}{B}[/tex]For example:
[tex]x-3y+12=0[/tex]Where the slope is:
[tex]\frac{-(1)}{-3}=\frac{1}{3}[/tex]As you can see, both lines has the same slope, so, they are parallel.
Remember!
- Two lines are parallel if they have the same slope.
- Two lines are perpendicular if the product of their slopes is -1.
