Brick Thickness Experiment
Thickness (layers) 2 4 6 8
Breaking Weight (pennies)15 30 50 65
a. Plot the data. Draw the line for the data.
b. Find an equation for the line you drew
c. Use your equation to predict the breaking weights of paper brideges 3,5 and 7 layers thick
To plot the data and draw the line, you will need a graph or chart. On the x-axis, you will represent the "Thickness" values, and on the y-axis, you will represent the "Breaking Weight" values.
a. Plotting the data and drawing the line:
1. On the x-axis, mark the values 2, 4, 6, and 8 for the Thickness of the brick.
2. On the y-axis, mark the corresponding Breaking Weight values: 15 pennies for thickness 2, 30 pennies for thickness 4, 50 pennies for thickness 6, and 65 pennies for thickness 8.
3. Plot the points (2, 15), (4, 30), (6, 50), and (8, 65).
4. Connect the points with a straight line that passes as close as possible to all of them.
b. Finding an equation for the line:
The equation of a straight line can be written in the form y = mx + b, where y is the dependent variable (Breaking Weight), x is the independent variable (Thickness), m is the slope of the line, and b is the y-intercept. To find the equation for the line you drew, we need to find the values of m and b.
1. Calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line.
- Choose two points, such as (2, 15) and (8, 65): m = (65 - 15) / (8 - 2) = 50 / 6 = 25/3.
2. Calculate the y-intercept (b) by substituting the values of m, x, and y from any point on the line into the equation:
- Using the values (x, y) = (2, 15): 15 = (25/3)(2) + b.
- Simplify the equation: 15 = 50/3 + b.
- Solve for b by rearranging the equation: b = 15 - 50/3 = 45/3 - 50/3 = -5/3.
3. Write the equation of the line: y = (25/3)x - 5/3.
c. Using the equation to predict breaking weights:
To predict the breaking weight of paper bridges with thicknesses of 3, 5, and 7 layers, we can substitute these values into the equation obtained in step b.
1. For a thickness of 3 layers: y = (25/3)(3) - 5/3 = 75/3 - 5/3 = 70/3 pennies.
2. For a thickness of 5 layers: y = (25/3)(5) - 5/3 = 125/3 - 5/3 = 120/3 pennies.
3. For a thickness of 7 layers: y = (25/3)(7) - 5/3 = 175/3 - 5/3 = 170/3 pennies.
Therefore, we predict that the breaking weights of paper bridges 3, 5, and 7 layers thick are approximately 70/3, 120/3, and 170/3 pennies, respectively.
You need to follow the question and plot the data. Plot weights (y) against thickness (x).
Then draw a best fit line through the points.
This line will pass through (0,c) and have a gradient m, both of which you can determine from the graph.
The equation of the line is then
y=mx+c
Substitute the values 3,5 and 7 in the equation (x values) and find the corresponding weights (y values).
Does this help?