1. Parallel Lines and Slope

2. Parallel Lines equal. ... The slopes of parallel lines are Example:
The rate of change of parallel lines is the same.

3. Note: The y-intercepts Normally are Not the Same
99.9% of the time, if two lines are parallel or perpendicular, they will NOT have the same y-intercept. (In fact, only RARELY do perpendicular lines share a y-intercept. If lines with the same slope have the same y-intercept, the lines coincide and are not parallel.)

4. Example: Parallel Lines
Algebraically find the equation of the line that goes through the point (16,4) and is parallel to 3x + 4y = 8.
Find the Slope
Find the y-intercept.
Use Slope-Intercept Form:
The slope is -3/4
A point on the graph is x=16 and y=4
The equation now has one distinct variable. Solve it.
Since Parallel Lines have the same slope, our new equation also has slope -3/4. (This y-intercept does not matter)
Substitute back into Slope-Intercept Form: