This table shows the linear relationship of the water level in a tank and time.
Time (hr) Water level (ft)
0 50
2 40
4 30
6 20
By examining the values given in the table, we can determine the linear relationship between the water level in the tank and time.
If we observe that at time 0, the water level is 50 ft, and after every 2-hour interval, the water level decreases by 10 ft, we can infer that the water level is decreasing at a rate of 10 ft per 2 hours or 5 ft per hour.
Using this information, we can establish the linear relationship between the water level (L) and time (T) using the slope-intercept form of a linear equation, y = mx + b, where y represents the water level, x represents time, m represents the slope, and b represents the y-intercept.
Given that the slope (m) is -5 ft/hr (since the water level is decreasing), we can determine the equation as follows:
L = (-5)T + b
To find the y-intercept (b), substitute the values from the table into the equation and solve for b.
When T = 0 (at the beginning, time is 0), L = 50 ft:
50 = (-5)(0) + b
50 = 0 + b
b = 50
Therefore, the equation that represents the linear relationship between the water level and time is:
L = -5T + 50