**Equation of a set of points**

Find all points (x, y) in a plane that are equidistant from the x and y axes.

There are at least (1,1), (2,2), (3,3) and so on number of such points.

All such points would appear to form a straight line.

The equation of the set of points is y = x. This includes all points that are equidistant from both the x and y axes.

**Example 1**

The equation for a set of points is * 2x + 3y - 6 = 0* What kind of graph do the set of points form?

Solution

Find pairs of points by assigning values to the variable x.

When* x = 0, *the equation of the set of points is * 3y - 6 = 0,* which gives* y = 2*

When* x = 3, *the equation of the set of points is *6 + 3y - 6 = 0*, which gives *y = 0*

When *x = 6,* the equation of the set of points is *12 + 3y - 6 = 0,* which gives* y = -2*

Point pairs* (0,2), (3,0) *and* (6, -2)* are obtained

The points sit on the same line. If we continued to solve more points, they would sit on the same line. The graph from the set of points equation is a straight line.

**Example 2**

Below is the equation for a set of points. Does point* (2,3)* belong to the set of points?

Solution

substitute the point* (2,3)* into the equation of the set of points.

The equation is false, so the point *(2,3)* does not belong to the set of points.

**Example 3**

What must be the value of* y* at the point* (2, y)* for the point to belong to the set of points in Example *2*?

Solution

We substitute *x = 2* into the equation of the set of points.

The points that belong to the set of points when *x = 2* are

The equation of a set of points includes all the points of the plane* (x, y) *that follow the rule given by the equation between *x *and* y.*