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Math Help - slope and y-intercept.

  1. #1
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    slope and y-intercept.

    1. Slope: -2; y-intercept: (0, 4)


    2. Slope: -3/4; y-intercept: (0, 8)



    3. Driving down a mountain, Tom finds that he has descended 1800 ft in elevation by the time he is 3.25 mi horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundredth.
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  2. #2
    Senior Member ecMathGeek's Avatar
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    What are you supposed to do with 1) and 2)

    3) The equation for the slope is m= (rise)/(run) = (change in y)/(change in x)

    The 'change in y' is -1800 ft (it's negative because he decended)
    The 'change in x' is 3.25 miles = 3.25*(5280ft) = 17160ft

    m = -1800/17160 = -0.104895 ... when rounded to the nearest hundredth = -0.10
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  3. #3
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    slope and y-intercept

    sorry for the confusion.
    equation 1 & 2

    Write the equation of the line with given slope and y-intercept. Then graph each line using the slope and y-intercept.


    I can't seem to make a graph. So if you have any special techniques that you like to share I would appreciate it.
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  4. #4
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    These are lines, so use y=mx+b, where m is your slope and b is your y-intercept.

    A good way to draw it, is on your graph, mark the y-intercept and then in your equation set y=0 and solve it for x, that way you get your x-intercept also. Now that you have two points, draw the line through them. That is to say;

    y-intercept = (0,4) give in the question
    and
    slope = -2

    so your equation is;
    y= -2x + 4

    now find the x-intercept by letting y=0.
    0= -2x + 4
    2x = 4
    x = 2

    so your x-intercept is at (2,0)

    Now that you have your two points (0,4) and (2,0) draw your line through them.


    Do the same for the other.
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  5. #5
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by Patience View Post
    1. Slope: -2; y-intercept: (0, 4)


    2. Slope: -3/4; y-intercept: (0, 8)



    3. Driving down a mountain, Tom finds that he has descended 1800 ft in elevation by the time he is 3.25 mi horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundredth.
    2) Slope m=-3/4, y-intercept (0,8)

    The slope-intercept equation form of a line is:
    y = mx+b ... where m is the slope of the line and b is the y-intercept

    We can plug in the initial information: Slope m=-3/4, y-intercept (0,8), where b = 8, and we get:
    y = -3/4x+8

    Now, lets graph this. To graph the equation of a line, we have a few methods we can use:

    1) Create an xy-chart, were we plug in values for x and solve for the values of y, then we graph the points we get on an xy-plane and draw a line through them.
    2) Use the y-intercept (which we were given from the initial information, y-intercept (0,8)), then we can solve for the x-intercept by setting y=0 and solving for x. Graph both of these points then draw a line through them
    3) Use the y-intercept to graph one point, then use the slope of the line (m=-3/4) to find another point. Then, as always, draw a line between these points.

    I'll explain the process for using option 3).

    First, graph the y-intercept. Since the y-intercept is (0,8), just put your dot 8 units up on the y-axis.

    Second, use the slope m=-3/4 to find your next point:
    As I'm sure you know, slope equals 'rise over run' or 'change in y over change in x'. Since the slope is -3/4, the 'change in y' is (-3), and the 'change in x' is (4).
    From the y-intercept (0,8), move down 3 units, then move over 4 units, and make your next dot. Note: the point you should be at when you move down 3 and over 4 from the point (0,8) is (4,5). So the two points you should have graphed are (0,8) and (4,5).

    Now, just draw a line that goes through these points.
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