Question

The table shows a proportional relationship between the weight on a spring scale and the distance the spring has stretched.

a. Complete the table.

b. Describe the scales you could use on the x and y axes of a coordinate grid that would show all the distances and weights in the table.

distance (cm) weight (newtons)
20 28
55
140
1

Answer 1

See below

Explanation:

As per the first row of proportional relationship, the proportion is:

• y = kx
• 28 = k*20
• k = 28/20 = 1.4

The function is therefore:

• y = 1.4x

a) Table is filled in below:

distance (cm) | weight (newtons)

20 | 28

55 | 55*1.4 = 77

140/1.4 = 100 | 140

1 | 1*1.4 = 1.4

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b) The scale should consider the coefficient 1.4, therefore x- axis will have a scale of 100 with intervals of 1 cm and y- axis will have a scale of 140 with intervals of 1.4 newtons