Trevor is analyzing a circle, y2 + x2 = 100, and a linear function g(x). will they intersect?

Given a circle described by the equation:

and a function g(x) given by the table


The function g(x) describes a straight line with the equation:


To check if the circle and the line intersects, we substitute the equation of the line into the equation of the circle to see if we have a real solution.
i.e.


When x = 6, y = 2(6) - 20 = 12 - 20 = -8 and when x = 10, y = 2(10) - 20 = 20 - 20 = 0

Therefore, the circle and the line intersect at the points (6, -8) and (10, 0).

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