Question

Ross is analyzing a circle, y2 + x2 = 64, and a linear function g(x). Will they intersect?

Answer 1

g(x) is a linear function, so we just need the slope and a point on this line to find the equation

Answer 2

what's the slope of g(x)?

Answer 3

One sec

Answer 4

alright

Answer 5

The slope is .5?

Answer 6

good

Answer 7

what's the y-intercept?

Answer 8

-4?

Answer 9

or (0,-4), good

Answer 10

so what's the equation of g(x)?

Answer 11

g(x)=.5(-4)^x?

Answer 12

no

Answer 13

linear equations are of the form y = mx + b

Answer 14

m is the slope
b is the y-intercept

Answer 15

no
but the line goes through the point \((0,-4)\) which is inside the circle

Answer 16

that's a good point, if you have a point in the circle (that lies on the line), then the line has to cross through the circle since it goes on forever

but it often helps to figure out the equation

Answer 17

g(x)=.5(-1)-4?

Answer 18

more like g(x) = 0.5x - 4

Answer 19

since m = 0.5 (slope) and b = -4 (y-intercept)

Answer 20

Oh ok. Let me graph them to see if they intersect at more than one point

Answer 21

Ok so they intersect at both a negative and a positive x-coordinate?

Answer 22

that is correct

Answer 23

Awesome. Thanks Jim :)

Answer 24

sure thing

Answer 25

@jim_thompson5910 what if the line intersects with the circle when x=0, will the answer still be they intersect at both a negative and a positive x-coordinate, if 0 is neither positive nor negative?!

Answer 26

@mathlover2014
@mtbender74