The graph of the pool's water level as a function of time is a straight line with a slope of 6, reflecting a constant rate of increase. The initial water level is 100 centimeters, and after 20 minutes, it reaches 220 centimeters.
To graph the pool's water level as a function of time, we can use the equation of a linear relationship, where the water level (y) is a function of time (x). The equation for this scenario is y = mx + b, where m is the rate of change and b is the initial amount.
Given that the water level rises at a rate of 6 centimeters per minute, the slope (m) is 6. We know that after 20 minutes, the water level is 220 centimeters, so we can use this information to find the y-intercept (b). Substituting the values, we get 220 = 6(20) + b, which gives b = 100.
Now, the equation representing the water level as a function of time is y = 6x + 100. This linear equation can be plotted on a graph, where the x-axis represents time (in minutes) and the y-axis represents the water level (in centimeters). The slope of 6 indicates a constant rate of increase, and the initial value of 100 represents the starting water level.
The graph will be a straight line sloping upwards from left to right, indicating a steady increase in the water level over time.