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0 / 5. 0 Category: Problem solving

Subcategory: Mathematics

Level: College

Pages: 2

Words: 550

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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