Question

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
a
Yes, at positive x-coordinates or zero

b
Yes, at negative x-coordinates or zero

c
Yes, at negative and positive x-coordinates or zero

d
No, they will not intersect

Answer 1

Ok lets see. What do you know about graphing?

Answer 2

Ok so \[g(x)=-3x+6\]

Answer 3

hmph joe ur mean I wanted to help but ill let you

Answer 4

if you still want my help?

Answer 5

Joe is just making it more complicated than it has to be

Answer 6

true true sorry

Answer 7

you can just calculate it on desmos.com
\[y^2+x^2=16\]
\[(0,6)\]
\[(1,3)\]
\[(2,0)\]

Answer 8

You just need to plot the three points they gave and draw a line through it and see whether or not it intersects the circle. If so, where does it intersect? Is it going to be a positive x-coordinate, negative x-coordinate or at 0?

Answer 9

but you never know if they can't do that traq so I was trying to give them another option.

Answer 10

You didn't even explain where you got g(x) = -3x + 6

If they can't plot points, they won't have any idea that you're determining the equation for those set of points and then trying to find the point(s) at where the circle and line intersect

Answer 11

on a calculator you can just press y= and type the equation

Answer 12

I know that but that doesn't solve an equation by inputting it

Answer 13

Okay so like on the Y value it decreases by 3 each time til it reaches 0 while x increases by 1 so when i plugged in for x i just add the total value of y and divided by 3 for x

Answer 14

but you seem to got it so i advise you to help them out🤷

Answer 15

you just switched from explaining how to calculate "it" on desmos to how you determined the equation
got me all confused for a second

Answer 16

@wrkwhrkhr can you graph the points (0, 6) and (1, 3) and (2, 0) on this

Answer 17

I was trying to work on the other solution in case they couldn't access that or something

Answer 18

There's only one solution

Answer 19

I meant other ways to solve for the solution

Answer 20

As for @ukulelegirl and @joe348 ,thank you as well for trying to help at your best possible way;I present you both an imaginary medal.As for @tranquility ,thank you for your time and patience,throughout.

Answer 21

Draw a line between those three points

Does that line go through the circle?

Answer 22

Exactly. You get something like this

Answer 23

Yes,totally;thank you so much for the clarification .I just needed a guide to see if I was on track,I just need more confidence in my mathematical skills;thank you again.

Answer 24

To choose your final answer, you need to say whether it's a positive or negative x-value for where it will intersect

Hopefully this will help you (if you haven't already figured it out)

Answer 25

Well from my overall knowledge of graphing and such,the slope of the line if falling so would it be negative in outcome...@tranquility ...?

Answer 26

The line has a negative slope, that's correct. However, we're trying to see at what x-values the line and the circle intersect

Answer 27

I've drawn an arrow to the two places at where they intersect

Is that a positive or negative x-coordinate

Answer 28

(forgot to attach the image in my previous reply but for future reference)

Answer 29

Well thank you @tranquility ,it is highly appreciated.Have a good rest of your day.

Answer 30

It was my pleasure! You too!