Question

Find the rate of change between the two points. Give the units of measure for the rate. \((53,44)\) and \((32,14) ; x\) in seconds, \(y\) in liters.

Short answer

The rate of change or slope between the two points is \(10/7\) litres per second.

Step-by-step solution

Identify the coordinates

Identify the coordinates of the two points. The first point is (53,44) and the second point is (32,14). It means the first point at time 53 seconds, the volume is 44 liters and at time 32 seconds, the volume is 14 liters.

Calculate the differences

Calculate the differences in both the x-coordinates and the y-coordinates. The difference in x-coordinates \(Δx\) is \(53 - 32 = 21\) seconds. The difference in y-coordinates \(Δy\) is \(44 - 14 = 30\) liters.

Compute the rate of change

Compute the rate of change which is the slope of the line passing through the two points, by dividing the difference in y-coordinates by the difference in x-coordinates. \(Rate = Δy / Δx = 30 litres / 21 seconds = 10 / 7 litres/second.\)