Thursday, 3 July 2014

Homework: Study Notes (p30) Discussion 1

How would you determine if the points A (2, -5) and B (5, 2) lie on the straight line y = 3x - 5?

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17 comments:

  1. This comment has been removed by the author.

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  2. A is obviously not on the line. -5 is the y intercept, thus if A is on the line, the coordinates would be (0, -5)

    To find out if B is on the line, substitute -5 as c. Then substitute x and y with the coordinates in B. If x and y is on the line, c=5 would be found.

    Grp 3

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  3. We can substitute the y and x in y=3x-5 with the x and y points in A and B. So these are the workings:

    A:
    y=3x-5
    -5=(3x2)-5
    -5=6-5
    -5=1
    Since -5 does not equal to 1, then point A is definitely not on the straight line.

    B:
    y=3x-5
    2=(5x3)-5
    2=15-5
    2=10
    Since 2 does not equal to 10, then B is not on the line.

    Group 1

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  4. If A and B both lie on the straight line, all we need to do is to calculate the gradient using (2, -5) and (5, 2) to see if the result agrees with the equation.

    m = (-5-2)/(2-5)
    = 7/3

    The calculated gradient with the 2 points A and B is 7/3. But, the equation states that the gradient is 3, so the 2 points are not on the line.

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  5. To find out is A and B is on the line, we can just substitute in the coordinates into the equation.

    For Point A, the coordinates are (2,-5)
    So the equation is y=3x-5,
    therefore the equation will become:
    -5=3(2)-5
    -5=6-5
    -5≠1
    We can easily conclude that A does not lie on the graph.

    For B, we can also use the same method. B's coordinates are (5, -2)
    So the equation will become
    -2=3(5)-5
    -2=15-5
    -2≠10

    Again, we also can easily conclude that B is also not on the line.

    Group 4

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  6. How would you determine if the points A (2, -5) and B (5, 2) lie on the straight line y = 3x - 5?

    We can substitute the coordinates into the equation. In A, we can the substituted equation is -5=3(2)-5. The equation obviously does not match. Both sides of the equation are unequal. Thus, A is not the point on the line.

    Next, for B, the equation will be 2=3(5)-5 which is 2=10. The equation is invalid once again, and we can conclude that B is not a point on the graph.

    Group 2

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  7. we can subsitute the actual numbers to the equations
    it would look like "-5 = 6 - 5" and this is obviously wrong, hence A does not lie on the line

    for B it will look like "2 = 15 - 5" which is once again wrong since it does not add up, hence B does not lie on the line

    group 1

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  8. In order to solve this, we just need to substitute the points into the equation… If the points satisfy the equation, the the points do sit on the straight line, y=3x-5.

    So here is my attempt to solve this question:

    For ordered pair (2,-5),

    y=3(2)-5
    =6-5
    =-1,
    Therefore, since (y) is (-1) and not (-5), this ordered pair does not satisfy the equation y=3x-5 and hence, this coordinate does not lie on the equation of the straight line.

    For ordered pair (5,2),

    y=3(5)-5
    =15-5
    =10,
    Therefore since (y) is (10) and not (2), this ordered pair does not satisfy the equation y=3x-5 and hence, this coordinate does not lie on the equation of the straight line.

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  9. We can substitute y=mx+c with y=3x-5 If both points A and B lie on the same line, we can just find the gradient of a and b: m= (-5-2)/(2-5)= 2 1/3

    The calculated gradient with the 2 points A and B is 2 1/3. But the gradient stated in the question is 3 thus, point A and B are not on the straight line.

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  10. How would you determine if the points A (2, -5) and B (5, 2) lie on the straight line y = 3x - 5?

    Using y=mx +c ,
    m = gradient
    = y1-y2
    -------------
    x1-x2

    = -5 - 2
    ------------
    2 - 5

    = -7
    -------------
    -3
    = 2.33 (3 sf)

    y= mx+c
    y = 2.33 x + -5

    Thus , points A and B are not on the same line.

    Group 4

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  11. A) y=mx+c
    If (x,y) = (2,-5)
    -5=3(2)-5
    =1

    Since the answer is not 0 the coordinates do not lie on the line.

    B) if (x,y) = (5,2)

    then 2=3(5)-5

    =10

    so it is also not on the line as any point that lies on the line must have a final answer of 0 after being simplified.

    Group:4

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  12. POINT A =(2,-5)
    So y=3x-5,
    thus -5=3(2)-5
    -5=6-5
    -5≠1
    SO obviously Point A is not on the Line

    Point B(5, -2)
    So -2=3(5)-5
    -2=15-5
    -2≠10

    SO Point B is also not on the line

    Grp 3 :D

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  13. Point A=(2,-5)
    Substitute x & y coordinates with x & y in y=3x-5
    Thus, y=3x-5
    =-5=6-5
    -5=1 which is wrong, so A is not on the line

    Point B can also be done with this method

    y=3x-5
    2=15-5
    2=10 which is again wrong

    Both points A and B are not on the line y=3x-5

    Group 1

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  15. In order for both points A and B to line on a straight line, their gradient* has to be the same as the given line. Hence, we calculate the gradient:
    (2 (-5)) / (5 - 2) = 7/3

    As you can see, the gradient of the given line and *[the gradient of the line made when points A and B are joined] are not the same. Thus points A and B do not lie on the line.

    Group 3

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