Straight Line Circle

How do I prove that a straight line does not meet a circle?

These are not the real equations (I do want to learn something from this question), but they work because I tried them on omnigraph (I learn best from examples):
y=x+4
(x-4)^2 + (y+1)^2 = 16

(x – 4)² + (x + 5)² = 16
x² – 8x + 16 + x² + 10x + 25 = 16
2x² + 2x + 25 = 0
x = [ - 2 ± √ (4 - 200 ) ] / 4
Has no real solutions
Thus line does not intersect circle.

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