To graph the lines of equation ax + by + c = 0 (b0), we isolate the variable y and assign values to x, obtaining ordered pairs that are points of the line. Thus, it is more convenient to use the equation in reduced form as it presents the isolated y.
Coordinates of the point of intersection of lines
The intersection of the lines r and s, when it exists, is the point P(x, y), common to them, which is the solution of the system formed by the equations of the two lines. Let's determine the intersection point, for example, of the lines r: 2x + y - 4 = 0 and s: x -y + 1 = 0. Setting up the system and solving it, we have:
Overriding this value at x -y = -1, we have:
1 - y = -1
y = 2
Soon, P(1, 2) is the intersection point of the lines r and s.
Graphically, we have:
Next: Relative Positions Between Lines