The key feature of the functions that are needed to determine if the lines intersect are;
- The slope; rate of change
- The y-intercept
Slope and y-intercept
From straight line geometry, we can conclude that two parallel lines whose slope are equal can never intersect.
On this note, for the functions described in the question, the functions only intersect when the slopes are different.
Additionally, the functions may intersect in the event of having equal y-intercepts.
In order two straight lines in a coordinate plane intersect, they MUST have different slopes.
This condition is NECESSARY and SUFFICIENT.