Answer:
Here's what I get
Step-by-step explanation:
Question 1
(a) Plot the data
The data are the represented by the green dots in the first diagram below. The horizontal axis is the number of layers and the vertical axis is the breaking weight.
(b) Draw the best-fit line
The best-fit line should go as close as possible to all the points and have about half the points above the line and half below.
If I join the first and last points, then I will have two points on the line, one above, and one below.
See the solid green line in the diagram.
(c) Write the equation for the line
The equation for a straight line is
y = mx + b
where m = the slope and b = the y=intercept.
When I extend the line backwards, it appears to cut the y-axis at about (0, -2), so
b = -2
[tex]\text{Slope} = \dfrac{\text{Change in y}}{\text{Change in x}}= \dfrac{y_{2}-y_{1}}{ x_{2}-x_{1}}[/tex]
Choose two points that are on the line (2, 15) and (8, 65). Then
[tex]\text{Slope} = \dfrac{65-15}{8-2} = \dfrac{40}{6} = \mathbf{\dfrac{25}{3}}[/tex]
The equation for the line is
[tex]\mathbf{y} = \mathbf{\dfrac{25}{3}x - 2}[/tex]
(d) Use the graph to make predictions
Start at a given value of x. Draw a line vertically upwards until you hit the graph. Then, draw a horizontal line until you hit the y-axis
(i) Three layers
I estimate breaking strength at about 24 pennies (red arrows).
(ii)Five layers
I estimate breaking strength at about 40 pennies (blue arrows).
(iii)Seven layers
I estimate breaking strength at about 56 pennies (orange arrows).
Question 2
(a) Modelling data
Student 1 has three points on the line and two fairly close to it.
Student 2 has only one point on the line, with three of the points further from the line and on the same side
Student 1 models the data better.
(b) Modelling data
See the second diagram below.
(i) Graph A
The graph has most of the points close to the line. Two points are above the line and one below, but the lower point is further from the line, so it compensates for the two above.
(ii) Graph B
The graph tries to split the difference between the points.
(iii) Graph C
No points on the line, but five are above and five below.
Note: These are all eyeball estimates. Your estimates may be different from mine.
