Equation of Lines Parallel To X-Axis And Y-Axis
Consider the equations x = 3. If this is treated as an equation in one variable x, then it has the unique solution x = 3 which is a point on the number line.
However when treated as an equation in two variables and plotted on the coordinate plane it can be expressed as x + 0.y - 3 = 0
This has infinitely many solution, let us find some of them.Here the coefficient of y is zero.So for all values of y,x becomes 3.
| x | 3 | 3 | 3 | 3 | 3 | 3 | ... |
|---|---|---|---|---|---|---|---|
| y | 1 | 2 | 3 | -1 | -2 | -3 | ... |
| (x,y) | (3,1) | (3,2) | (3,3) | (3,-1) | (3,-2) | (3,-3) | ... |
| Points | A | B | C | D | E | F | ... |
From the table it is clear that this equation has infinitely many solutions of the form (3, a) where a is any real number.
Now draw the graph using the above solutions. What do you notice from the graph?
Is it a straight line? Whether it is any line or axes?
The line drawn is a straight line and is parallel to Y-axis?