Question

Terrence is folding paper cranes at a constant rate. The table below shows the amount of time he needs to fold cranes.

Number of cranes Total time (minutes)
555 17.517.517, point, 5
888 282828
121212 424242
Write an equation to describe the relationship between ccc, the number of cranes, and ttt, the total time in minutes.

Answer 1

t=3.5c

Explanation:

Answer 2

t = 3.5c

Explanation:

The correct table is attached in the image below. Since the papers are being folded at a constant rate, there is a linear relationship between c, the number of crane and t, the total time in minutes.

We can find the equation of this linear relation using any two pair of points from the table. Using the first two points: (5, 17.5) and (8, 28)

First we need to find the slope of the line which gives the relation between the two variables.

`Slope=\frac{\text{Difference in y coordinates}}{\text{Difference in x coordinates}}`

y coordinates represents the dependent variable which is the time in this case and x coordinates represents the independent variable which is number of cranes in this case. Using the values from the two points we considered:

`Slope=(28-17.5)/(8-5)=3.5`

Thus, the equation of the line will be of the form:

t = mc + b

m is the slope here. Using its values, we get:

t = 3.5c + b

b is known as y-intercept. We need the value of b to complete the equation. Substituting the value of t and c from any pair we can find the value of b.

Using the point (5, 17.5), we get:

17.5 = 3.5(5) + b

b = 0

This means, the equation of the line would be:

t = 3.5c