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Math Help - Gradient

  1. #1
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    Question Gradient

    A line goes through the points x = -2, y = 5 and x = 1, y = 17. What is the gradient of this line?
    a) -4
    b) 5.33
    c) 12
    d) 4
    e) 0.25

    Hi, this is the next question I am stuck on, how is this worken out?
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  2. #2
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    Quote Originally Posted by chungkayan View Post
    A line goes through the points x = -2, y = 5 and x = 1, y = 17. What is the gradient of this line?
    a) -4
    b) 5.33
    c) 12
    d) 4
    e) 0.25

    Hi, this is the next question I am stuck on, how is this worken out?
    The gradient of the line through the points (x_1,y_1) and (x_2, y_2) is:

    m=\frac{y_1-y_2}{x_1-x_2}

    CB
    Last edited by CaptainBlack; October 30th 2009 at 05:37 PM.
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  3. #3
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    Hi, I am a bit slow. so its -3/-12?=1/4?

    The answer should be 4 though?
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  4. #4
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    how about this, is this, is it any similar?
    A straight line has the equation y = 0.5x - 12 . Which of the following is true?
    a) Its gradient (slope) is ˝ and y-intercept 12
    b) Its gradient (slope) is 12 and y-intercept 0.5
    c) Its gradient (slope) is ˝ and y-intercept -12
    d) Its gradient (slope) is -0.5 and y-intercept 12
    e) Its gradient (slope) is 2 and y-intercept -12
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  5. #5
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    Quote Originally Posted by chungkayan View Post
    Hi, I am a bit slow. so its -3/-12?=1/4?

    The answer should be 4 though?
    There is a typo in the earlier post see that.

    CB
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  6. #6
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    Question

    Hi, what typo? typo mistake?



    I get it now.

    m= -12(y answer)/-3(x answer)=4! yay! plenty of thanks! thats the formula for finding out this equation?
    -

    how about this, i cant find it using that?
    is there another formula for this?
    2. A straight line has the equation y = 0.5x - 12 . Which of the following is true?
    a) Its gradient (slope) is ˝ and y-intercept 12
    b) Its gradient (slope) is 12 and y-intercept 0.5
    c) Its gradient (slope) is ˝ and y-intercept -12
    d) Its gradient (slope) is -0.5 and y-intercept 12
    e) Its gradient (slope) is 2 and y-intercept -12

    & also this:
    3. A firm’s profit function is given by: Profit = x2 –7x –30 where x is the number of units sold. What is the firm’s break-even point?
    a)3
    b)10
    c)7
    d)13.5
    e)88

    Is this how u work out the 3rd question:
    30=x(squared)-7*x(squared), which is 10. since 10*10=100-(7*10=)70, and 100-70=30, which is the break even point?

    Or am i taking it too easy?
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  7. #7
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    Quote Originally Posted by chungkayan View Post
    Hi, what typo? typo mistake?



    I get it now.

    m= -12(y answer)/-3(x answer)=4! yay! plenty of thanks! thats the formula for finding out this equation?
    -

    how about this, i cant find it using that?
    is there another formula for this?
    2. A straight line has the equation y = 0.5x - 12 . Which of the following is true?
    a) Its gradient (slope) is ˝ and y-intercept 12
    b) Its gradient (slope) is 12 and y-intercept 0.5
    c) Its gradient (slope) is ˝ and y-intercept -12
    d) Its gradient (slope) is -0.5 and y-intercept 12
    e) Its gradient (slope) is 2 and y-intercept -12
    If a line is written as "y= mx+ b" (called the "slope-intercept form"!) then the slope is m and the y-intercept is b.

    & also this:
    3. A firm’s profit function is given by: Profit = x2 –7x –30 where x is the number of units sold. What is the firm’s break-even point?
    a)3
    b)10
    c)7
    d)13.5
    e)88

    Is this how u work out the 3rd question:
    30=x(squared)-7*x(squared), which is 10.
    What do you mean "which is 10"? You just wrote that that was equal to 30!
    Okay, you mean that x= 10 satisfies x^2- 7x- 30= 0. That means that when produce 10 units, you make $0 profit. You don't make any profit but you don't lose money either. That's what "break even point" means!

    since 10*10=100-(7*10=)70, and 100-70=30, which is the break even point?

    Or am i taking it too easy?
    Well, you seem to be ignoring definitions! You did all the algebra correctly but aren't able to decide what the answer to "what is the break even point", perhaps because you don't know what "break even point" means! Look at the definition. Then you should be able to see that you already have the answer.
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  8. #8
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    Smile

    thanks so much! I get it now. this really helped alot.

    It means its gradient (slope) is ˝(m) and y-intercept -12(b). no working out is needed for this then? since using that slope-intercept form, y=mx+b gives you the answer straight away.

    Thanks again! =)

    Last edited by chungkayan; November 1st 2009 at 02:08 AM.
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