Given each equation, find the slope, the parallel slope, and the perpendicular slope
1.Y=2X+5
2. y=1/3x
3.y=2
4. 5x =2y=6
5.-4-7Y=9
The slope of a line is defined as the change in y divided by the change in x; that is:
\(\displaystyle m := \frac{\Delta y}{\Delta x}\)
It so happens that in an equation \(\displaystyle y = mx + b\), m is already solved. Therefore, you have the slope of 1-3 given to you. In 4-5, just solve for y.
When you have a line in the equation \(\displaystyle y = mx + b\), then \(\displaystyle m\) is the slope of all parallel lines.
Furthermore, \(\displaystyle -\frac{1}{m}\) is the slope of the all the perpendicular lines
I am going to work out an example:
\(\displaystyle 3y - 2x + 2 = 3x + 4\)
Add \(\displaystyle 2x\): \(\displaystyle 3y + 2 = 5x + 4\)
Subtract \(\displaystyle 2\): \(\displaystyle 3y = 5x + 2\)
Divide by \(\displaystyle 3\): \(\displaystyle y = \frac{5}{3}x + \frac{2}{3}\)
Meaning \(\displaystyle m = \frac{5}{3}\). All equations with this slope are parallel.
The perpendicular slope is \(\displaystyle -\frac{3}{5}\)
