A bag is hanging from the table top on to one side. As washers are added to the bag, the lower end of the bag moves down due to weight (perhaps). There is some elastic material which is connected to the bag. It gets stretched perhaps. Washers are used as weights perhaps. This could be the graph representing the Hook's law in physics.

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I assume that the data plotted on the graph (grid paper) is applicable to
the first five questions. Otherwise, We do not have any other data.

1. You
are supposed to analyse the data. Form the domain and range. Check which
is independent variable and which is dependent variable. Observe the maximum
value - minimum value (span) of the two variables. That will help selection of scaling on the
graph. All this has been already done and graph is plotted.

From the table below you can form ordered pairs like (0, 8cm), (1, 9.25cm) etc.

Washers
number
0 1 2 3 4

Distance
in cm 8 9.25 10.5 12 13

Domain is [0, 4] Range is [8, 13]

Graphing is already done.

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2. Now it seems the points are falling on a straight line. If you want to apply the least squares method and find the best fit straight line for these points, it is okay. Otherwise, if our scope is not that high, then take a transparent scale and draw a straight line such that it is very close to all the points.

*Description : The distance increases linearly with the number of washers. ** or, the increase in distance is proportional to increase in number of washers. or, rate of change in distance wrt the number of washers is a constant (almost).*

in coordinate geometry or algebraic terms ,

distance = d = [ (13.1 - 8) /4 ] * w + 8 cm

d = ( 1.275 w + 8 ) cm

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3. The point on the vertical axis of distance marked at 8 is the point, that represents the trial when there are no washers in the bag.

(as number of washers is 0 for this point/trial )

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4. rate of change = increase in distance of the lower end of the bag from the table top / number of washers added.

See the table below:

1 Distance 8 9.25 10.5 12 13

2 change in distance 0 1.25 1.25 1.5 1

3 {number of washers} 0 0 1 2 3

{previously in the bag}

4 washers added 0 1 1 1 1

Rate of change is given by the second row, as one washer is added each time.

Using the algebra and geometry, rate = slope = 1.275 cm per one washer

5. If you join the successive points by straight lines. For each pair of successive points, draw a right angle triangle, with horizontal line from lower left point. The rate is equal to the slope of the line.

Rate = number of grid lines in the vertical direction / number of grid lines in the horizontal direction, in moving from one point to the next.

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6. see diagram.

The blue data points and graph line is the answer.

data points are (0, 10.5cm), (1, 11.75cm), (2, 13cm), (3, 14.5cm), (4, 15.5cm)

distance of lower end of bag from table top = d = (10.5 + 1.275 w ) cm

7. the data points are (0, 8cm), (1, 10 cm), (2, 12 cm), (3, 14cm), (4, 16cm)

d = (8 + 2 w) cm

8 data points are (0, 8cm), (1, 8.5cm), (2, 9cm) , (3, 9.5cm) (4, 10cm)

d = (0.5 w + 8) cm