The temperature of a liquid in an experiment starts at 0 degrees. The temperature of the liquid changes at a rate of - 0.2 per minute. How long will it take for the liquid to reach - 14.6 degrees.

Initial temperature of the liquid = 0 degrees.

Rate of changes of liquid temperature = - 0.2 per minute.

Rate of change also represents slope of a linear function.

We know, slope-intercept form of a linear equation

y=mx+b, where m is the slope (rate of change) and b is y-intercept (initial temprature).

With respect to given problem, y represents temperature of a liquid after x number of minutes.

According to given problem, slope (rate of change) = - 0.2 per minute and y-intercept (initial temprature) = 0.

Plugging values of m and b in the above slope-intercept form of a linear equation. We get,

y=-0.2x+0

or y=-0.2x.

Final temprature is given - 14.6 degrees and we need to find time when temprature reach - 14.6 degrees.

As y represents temperature of a liquid, we need to plug y=-14.6 in above equation.

We get,

-14.6=-0.2x.

Dividing both sides by - 0.2.

-14.6/-0.2=-0.2x/-0.2

x=73.

We got 73 minutes.

73 minutes can be convert in hours.

We have 60 minutes in an hour.

Therefore, 73 = 60+13.

So, 1 hour and 13 minutes will it for the liquid to reach - 14.6 degrees.

In minutes answer is 73 minutes.