Question

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

Answer 1

Yes, at positive x coordinates

Answer 2

Yes,they will intersect at (0.686,3.941) and (2.914,-2.741)

Explanation:

Given the values that represent the function g(x) you can plot them directly on a graph tool and plot the function y²+x²=16 then visualize

You can also determine the equation of the linear function as then graph both equations on the graph tool

Finding gradient m

Given (0,6) and (1,3)

m=change in value of y/change in value of x

`m=(3-6)/(1-0) =(-3)/(1) =-3`

Finding the equation of the linear function

Taking points (2,0) and (x,y)

`m=(y-0)/(x-2) \\\\-3=(y-0)/(x-2) \\\\\\-3(x-2)=y-0\\\\\\-3x+6=y-0\\\\\\y=-3x+6`

From the graph,they intersect at

(0.686,3.941) and (2.914,-2.741)