Question

Sally is analyzing a circle, y2 + x2 = 9, and a linear function g(x). Will they intersect?

x g(x)
-2 -1
1 1
4 3

Answer 1

Find the linear function g(x) first. You are given three points on g(x):
(-2,-1), (1,1) and (4,3). You just need two points to find g(x).
Use the last two points to find g(x).

Answer 2

These are the answer choices

Yes, at positive x-coordinates.
Yes, at negative x-coordinates.
Yes, at negative and positive x-coordinates.
No, they will not intersect. @ranga

Answer 3

And the screenshot that I had provided shows the two different graphs which I have seen and tried to conclude that the correct answer choice was A.

Answer 4

First locate the points (1,1) and (4,3) on the graph and imagine a line passing through those two points. Where will the line intersect the circle?

Answer 5

yes @ranga

Answer 6

Look at the x-coordinates of the two points where the line intersects the circle. Are the x-coordinates both positive, both negative, one positive and one negative?

Answer 7

Point A is in the first quadrant where x is positive.
Point B is in the third quadrant where x is negative.
Therefore, the line intersects the circle at negative and positive x-coordinates.

Answer 8

Hey do you think you can help me with 2 more problems
@ranga

Answer 9

I can try one more.

Answer 10

How can 1/5x − 2 = 1/3x + 8 be set up as a system of equations?

5y − 5x = −10
3y − 3x = 24

5y − 5x = −10
3y + 3x = 24

5y + x = −10
3y + x = 24

5y − x = −10
3y − x = 24

Answer 11

Ignore the image! @ranga

Answer 12

1/5x − 2 = 1/3x + 8
can be set up as: y = x/5 - 2 and y = x/3 + 8
To get rid of the fraction multiply the first equation throughout by 5 and the second equation throughout by 3:
5y = x - 10 and 3y = x + 24
Bring x to the left hand side:
5y - x = -10 and 3y - x = 24