In a question it says Q The equation y43 decribes A A Vertic

In a question it says:

Q: The equation y=4/3 decribes:

A- A Vertical line

B- A horizontal line

C- A point on a graph

D- Y-coordinates of a point

The answer is (B) which is a horizontal line.

My question is how to did we figure that out that its a horizontal line and not the other ones?, and can you provide me an example for each option (A,B,C,D).

Solution

The standard equation of a straight line is y = mx + c

Comparing it with y = 4/3, we see that c = 4/3 and mx = 0

i.e we draw this line on the graph which passes through the point x = 0 and y = 4/3 (0,4/3) with the intercept c = 4/3. When you do so, you will get a line that is parallel to x axis passing through the point (0,4/3). Hence the answer is a horizontal line.

To memorize, you may want to remember that if there is no x in the equation, then it is a horizontal line and if there is no y (like x = 2/3), then it is vertical line. If there are both, then it is a slanting line (y = 5x or y = 3x + 2)

A point on the graph is represented by (3,0) or (0,5) or (0,4/3) and not by y = 4/3.

This is also the y co-ordinate of a point but only when we are talking of the one dimensional plane. If we are talking of x axis and y axis both, then we always mention y co-ordinate along with x co-ordinate