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.

x=half

step-by-step explanation: