# QUIZ 1

Quiz 1

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(i) Consider a graph of shown below.

Find the slope and equation of the line joining A and B.

Let A (1,-10) be (x1,y1) and B(-2,17) be (x2,y2).

Slope is give by change in y/ change in x

Thus in this case, it will be (y1-y2)/(x1-x2)

= (-10-17)/ (1-(-2))

=-27/3

=-9

Equation of the line joining A and B

Take any point in the line AB to be (x, y) and (1,-10)

Then Slope remain the same thus,

-9=(y+10)/(x-1)

-9x+9=y+10

Thus y=-9x-1

Find the slope and equation of the line joining A and C.

Let A (1,-10) be (x1,y1) and C(0,1) be (x2,y2).

To find the slope= (y1-y2)/ (x1-x2)

= (-10-1)/(1-0)

= -11

Equation of the line AC will be

Assume a point (x, y) in the line and c(0,1)

Then -11=(y-1)/(x-0)

-11x=y-1

Then y=1-11x

Find the y-coordinate of the point P with x-coordinate equal to 0.5 (x=0.5.)

The equation of the curve is y=x^3-12x+1

At x=0.5

Substitute 0.5 to x in the equation

Y= (0.5) 3-12*0.5+1

Y=0.125-6+1

Y= -4.875

Find the slope and equation of the line joining A and P.

Let A (1,-10) be (x1, y1) and P (0.5,-4.875) be (x2,y2)

Then the slope= (y2-y1)/(x2-x1)

=(-4.875-(-10))/(0.5-1)

=5.125/-0.5

= -10.25

The equation of the line AP

Assume a point in the line (x, y) and A(1,-10)

= -10.25=(Y+10)/(X-1)

Y+10=10.25-10.25X

Y=0.25-10.25X (Larson & Edwards, 2009)

(ii) Consider the function defined by

Find

The value -2 lie in f(x)=2x-1

Set the f(x)=0 then

2x-1=0

2x=1

X=0.5

…

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