Nellie is analyzing a circle, y2 + x2 = 25, and a linear function g(x). will they intersect? y2 + x2 = 25 g(x) graph of the function y squared plus x squared equals 25 x g(x) −7 −2 −6 −1 1 6

The linear function is given by the following table:
 -7    -2
 -6    -1
  1     6
 The equation of the line is:
 y = x + 5
 The equation of the circle is:
 y2 + x2 = 25
 Therefore we have the following system of equations:
 y2 + x2 = 25
 y = x + 5
 The solution is:
 x = -5, y = 0
 x = 0, y = 5
 Therefore, the line and the circle intersect at two points:
 (-5, 0)
 (0, 5)
 
 they will intersect at:
 (-5, 0)
 (0, 5)