Barbie is analyzing a circle, y2 + x2 = 16, and a linear function g (x). Will they intersect?

y2 + x2 = 16 g (x)

graph of the function y squared plus x squared equals 16

x g (x)

0 6

1 3

2 0

Yes, at positive x-coordinates

Yes, at negative x-coordinates or zero

Yes, at negative and positive x-coordinates or zero

No, they will not intersect

Yes, at positive x-coordinates.

Step-by-step explanation:

Finding the equation for g (x):

Slope = (3-6) / (1-0) = - 3

y-intercept = y value when x = 0 = 6.

So g (x) = - 3x + 6

Solve them simultaneously:

x^2 + y^2 = 16

g (x) : y = - 3x + 6

Substitute for y in the first equation:

x^2 + (-3x + 6) ^2 = 16

x^2 + (9x^2 - 36x + 36) = 16

10x^2 - 36x + 20 = 0

5x^2 - 18x + 10 = 0

x = [ - (-18) + / - sqrt ((-18) ^2 - 4 * - 18 * 10) ] / (5*2)

= (18 + / - sqrt 124) / 10

= (1.8) + / - 1,114

These 2 roots are both positive.