Relative positions of two lines in the plane

In this video I will explain the relative positions of two lines in the plane. The relative position has these forms:

• parallel: if at no time will they cut at one point.

• blotters: if at some point they will cut at one point.

To find out what relative position two lines have, we will have to take into account the following:

If we do it from the explicit equation of the line (y = mx + n):

1. if the slope (m) of the first equation is equal to that of the second, we will be faced with two parallel lines.

2. If the slope (m) of the first equation is different from the slope of the second, we will be faced with two secant lines.

If we find the relative position from the General equation for a straight line (ax + bx + c = 0):

1. If the quotient between the coefficients of x (a) is equal to the quotient of the coefficients of y (b), they will be two parallel lines.

2. If the quotient between the coefficients of x (a) is different from the quotient of the coefficients of y (b), they will be two secant lines.

If the lines are parallel, it will be necessary to check if they are straight linesmatching, that is, if they form the same line. To find out this we will have to add the quotient of the independent term (c). All this you will understand better with the video examples.

If you want to reinforce what you have learned in today's lesson, you will only have to do the printable exercises with their solutions that I have left you on the web. I hope they help you!