Here we will learn how to draw coordinate geometry graph.

When two variables x, y are related, the value(s) of one variable depends on the value(s) of the other variable. Let x, y be two variables related by 9x – 3y + 4 = 0. Then, y = 3x + \(\frac{4}{3}\). This gives the value of y corresponding to a value of x.

For x = 0, 1, -1, etc, we get y = \(\frac{4}{3}\), \(\frac{13}{3}\), \(\frac{-5}{3}\), etc.

Therefore, (0, \(\frac{4}{3}\)), (1, \(\frac{13}{3}\)), (-1, - \(\frac{5}{3}\)), etc,. are all values of the ordered pair (x, y) given by the relation y = 3x + \(\frac{4}{3}\). Every ordered pair of real numbers represents the coordinates of a point. So, we can always plot a point corresponding to a ordered pair of values of (x, y) satisfying a given relation between x and y. The collection of all the points corresponding to the ordered pairs (x, y) satisfying the relation between x and y, is the graph of the relation.

Graph of Linear Relations Between x, y:

The points with coordinates (x, y) satisfying the linear relation ax + by + c = 0 lie on a straight line. So, the graph of a linear relation ax + by + c between the variables x and y is a straight line. The graph can be constructed by plotting at least two points corresponding to two ordered pairs of values of (x, y) satisfying the relation and then joining the two points by a straight line.

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