Question

Can there be more than one point of intersection between the graphs of two linear equations ? Why or why not ?

Answer 1

When the lines have the same equation.

Explanation:

If you have different slopes at one point the lines will cross each other since they are not parallel. Afterwards they will continue indefinitely onward in either direction, forever not crossing again.

For two lines to be parallel they have to have the same slope. For example y= 2x and y= 2x +3 are parallel to each other since they have the same slope, even if the y intercepts aren't the same. But since the y- intercepts aren't the same the second equation will always have y values 2 greater than the first equation. So for their to be multiple points of intersection not only does the slope have to be the same but the y-intercept must be as well.