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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

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carlosego
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:

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

Step-by-step explanation:

The equation of circle is

[tex]y^2+x^2=25[/tex]                 .... (1)

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

The equation of g(x) is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-(-2)=\frac{-1-(-2)}{-6-(-7)}(x-(-7))[/tex]

[tex]y+2=1(x+7)[/tex]

[tex]y=x+7-2[/tex]

[tex]y=x+5[/tex]                          ....(2)

The function g(x) is defined as

[tex]g(x)=x+5[/tex]

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

[tex](x+5)^2+x^2=25[/tex]

[tex]x^2+10x+25+x^2=25[/tex]

[tex]2x^2+10x=0[/tex]

[tex]2x(x+5)=0[/tex]

[tex]x=0,-5[/tex]

Put x=0 in equation (2).

[tex]y=0+5=5[/tex]

Put x=-5 in equation (2).

[tex]y=-5+5=0[/tex]

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

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