a) To draw a graph representing the information with time in seconds on the x-axis and volume in cm³ on the y-axis, you can follow these steps:
- Create a set of axes with time (seconds) on the x-axis and volume (cm³) on the y-axis.
- Plot the given data points (20, 5), (40, 10), (120, 30), (180, 45), and (240, 60) on the graph.
- Connect the points with a straight line to represent the relationship between volume and time.
b) To write an equation showing the relationship between volume (V) and time (T), you can use the equation of a straight line, which is in the form of y = mx + c, where:
- y is the dependent variable (volume in this case).
- x is the independent variable (time in this case).
- m is the slope of the line.
- c is the y-intercept.
First, calculate the slope (m) using two points, for example, (20, 5) and (240, 60):
m = (y₂ - y₁) / (x₂ - x₁)
m = (60 - 5) / (240 - 20)
m = 55 / 220
m = 0.25
Now that you have the slope (m), you can write the equation:
V = 0.25T + c
To find the y-intercept (c), you can use one of the data points. Let's use (20, 5):
5 = 0.25 * 20 + c
5 = 5 + c
c = 5 - 5
c = 0
So, the equation showing the relationship between volume (V) and time (T) is:
V = 0.25T