Answer the following questions Your answers will have b in t

Answer the following questions. Your answers will have b in them.

a. Find the slope of the line.

slope=

b.. Find the equation of the line. Use y for the dependent variable.

c. Find the coordinates of the point C.

( , )

Line passes through two points ( 0, b) and ( 1,1)

slope = (1-b)/(1-0) = 1-b

Stand equation of ine: y = mx +c ---> y = ( 1-b)x +c

find c from using the point ( 1,1) ----> 1 = ( 1-b ) + c

c= b

Equation of Line : y = ( 1-b)x +b

To find the coordinates of C , find the point of intersection of y= x^2 and y = ( 1-b)x +b

x^2 = ( 1-b)x +b

x^2 - ( 1-b)x -b =0

Roots of equation : x= { 1-b + /- sqrt( (1-b)^2 +4b }/2 = ( 1- b +/- ( 1+b) )/2 = ( 1 -b -1 -b)/2 , ( 1-b +1 +b)/2

x = -b , 1

So, y = x^2 --> b^2 , 1

So, C = ( -b , b^2 ) we negect ( 1,1) as it is given point is inIInd quadrant