Show that for every cartesian line L on the cartesian plane

Show that for every cartesian line L on the cartesian plane there exist three real numbers a, b, and c such that L is given by the equation a middot x + b middot y + c = 0 and a^2 + b^2 notequalto 0. Use our definition of cartesian lines that should be used in high schools. Show that for every three real numbers a, b, and c such that a^2 + b^2 > 0, the equation a middot x + b middot y + c = 0 describes a cartesian line. Use our definition of cartesian lines that should be used in high schools.

Solution

1.Let us observe the straight line ax+by+c=0.Clearly. It will cut the x axis any y axis at -c/a and - c/b respectively and Slope is - a/b. Clearly for slope to be defined - a/b should not be equal to zero and also b shouldn\'t be zero. Thus we can observe that for the line to be defined a, b and c should be noon zero.

2 If we take ax+by+c=0 ee can see that it can be represented as y=-ax/b-c/a. this is of the y =mx+\"