Ross is analyzing a circle, y^2+x^2=64 and a linear function g (x), will they intersect?

X. G (x)

-1. - 4.5

0. - 4

1. - 3.5

Yes at positive x coordinates

Yes at negative x coordinates

Yes at positive and negative x coordinates

No, they will not intersect

Find what g (x) is

y intercept is - 4

slope is 1/2

so

y=1/2x-4

so sub that for y in other equation

(1/2x-4) ^2+x^2=64

1/4x^2-4x+16+x^2=64

times 4 bot sides

x^2-16x+64+4x^2=256

minus 256 both sides

x^2-16x+4x^2-192=0

5x^2-16x-192=0

factor

(x-8) (5x+24) = 0

set to zero

x-8=0

x=8

5x+24=0

5x=-24

x=-24/5

at x=-24/5 and 8

so at positive and negative coordinates