The graph of a line in the xy-plane passes through the point (1, 4) and crosses the x-axis at the point (2.0). The line crosses the y-axis at the point (0, b). What is the value of b?

Answer with step-by-step explanation:

The graph passes through both (1,4) and (2,0)

Thus it's slope is the difference of ordinates over difference of abscissae or -4

Thus the equation becomes y = -4x + b

This b is the required b

At x=2 ; y=0

Thus 0= -8 + b

b=8

where is the figure

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.