Question

Nellie is analyzing a circle, y2 + x2 = 25, and a linear function g(x). Will they intersect? y2 + x2 = 25 g(x) graph of the function y squared plus x squared equals 25 x g(x) −7 −2 −6 −1 1 6

Answer 1

The linear function is given by the following table:
 -7    -2
 -6    -1
  1     6
 The equation of the line is:
 y = x + 5
 The equation of the circle is:
 y2 + x2 = 25
 Therefore we have the following system of equations:
 y2 + x2 = 25
 y = x + 5
 The solution is:
 x = -5, y = 0
 x = 0, y = 5
 Therefore, the line and the circle intersect at two points:
 (-5, 0)
 (0, 5)
 Answer:
 they will intersect at:
 (-5, 0)
 (0, 5)

Answer 2

Answer:

Yes, they will intersect at (-5,0) and (0,5).

Step-by-step explanation:

The equation of circle is

$y^2+x^2=25$                 .... (1)

The graph of g(x) is passing through the points (-7,-2) and (-6,-1).

The equation of g(x) is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-(-2)=\frac{-1-(-2)}{-6-(-7)}(x-(-7))$

$y+2=1(x+7)$

$y=x+7-2$

$y=x+5$                          ....(2)

The function g(x) is defined as

$g(x)=x+5$

On solving (1) and (2), we get

$(x+5)^2+x^2=25$

$x^2+10x+25+x^2=25$

$2x^2+10x=0$

$2x(x+5)=0$

$x=0,-5$

Put x=0 in equation (2).

$y=0+5=5$

Put x=-5 in equation (2).

$y=-5+5=0$

It means both functions intersect at (-5,0) and (0,5).