Question

the graph shows the temperature of a liquid that is being heated during an experiment. three of the statements are true. which is not? the temperature of the liquid is increasing at a constant rate. at this rate, the temperature will rise 60° in a quarter hour. the temperature of the liquid changed at a unit rate of 4° per minute. at this rate, it would take less than 10 minutes for the temperature of the liquid to rise 52°.

Explanation:

Step1: Calculate the unit rate

The graph passes through the point \((6.5,26)\). The unit rate \(k\) (slope) of a line \(y = kx\) (since it passes through the origin \((0,0)\)) is given by \(k=\frac{y}{x}\). Substituting \(x = 6.5\) and \(y=26\), we get \(k=\frac{26}{6.5}=4\). So the temperature - time relationship is \(y = 4x\), which means the temperature is increasing at a constant rate of \(4^{\circ}\text{C}\) per minute.

Step2: Check the statement about a quarter - hour

A quarter - hour is \(15\) minutes. Using the equation \(y = 4x\), when \(x = 15\), \(y=4\times15 = 60\). So the temperature will rise \(60^{\circ}\text{C}\) in a quarter - hour.

Step3: Check the statement about \(52^{\circ}\text{C}\)

Using the equation \(y = 4x\), when \(y = 52\), we solve for \(x\). \(x=\frac{y}{4}=\frac{52}{4}=13\) minutes.

Answer:

The statement “At this rate, it would take less than 10 minutes for the temperature of the liquid to rise \(52^{\circ}\)” is NOT true.