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need step by step explanation.

A) (0,-8), B (4,0)

B) 2

C) y = 2x -8

Step-by-step explanation:

Given

calculate the coordinate of point A and B

for point A

Point A lies on y axis, so for point A, coordinate of X axis is 0.

we will put x = 0 in the given equation

to find y.

Thus, y coordinate of point A is -8.

Thus, coordinate of point A (0, -8)

Point B lies on x axis, so for point B, coordinate of Y  is 0.

we will put y = 0 in the given equation

to find x.

Thus x+2 = 0 or x-4 = 0

x = -2 or x = 4

but x cannot be -2 as x is on positive side of x axis, hence x can take only positive value

Thus, X coordinate of point B is 4

Thus, coordinate of point B(4, 0).

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The gradient of  of two points (x1, y1) and (x2,y2) is given by

gradient = (y2-y1)/(x2-x1)

Since we have point A and B as (0, -8) and (4,0)

Thus gradient = 0 -(-8)/4-0) = 8/4 = 2 (answer B)

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Equation of straight line in point slope form is given by

y = mx +c

where m is the gradient of line and

c is y intercept .

Y intercept is point on y axis where the straight line meets y axis.

As calculated above

We have gradient = 2  

c = -8 (co-ordinates of point A is only the y intercept)

Thus, equation of line AB

is y = 2x -8  Answer C.

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f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50