Find the equation of a circle with a center at (7, 2) and a point on the circle at (-2, -5).

Step-by-step explanation:

The standard form of a circle is

where x and y are points on the circle, h and k are the center, and r is the radius.  We have what we need to fill in everything but the radius, but we will solve for that like this:

Simplifying gives you

and

so

That means the equation for this circle is

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: