Chapter 1.7, Problem 87PPE

To determine

To identify: the function as linear or non-linear, estimate and interpret the intercepts of graph.

Explanation of Solution

Given:

  

Here, x - axis represents time in hours.

y - axis represents Temperature in ${}^{\circ }F$

When the graph is interpreted it is clearly observable that the graph is a straight line and as the time increases the temperature keeps on falling at a constant rate and all the values of time has a unique temperature value which means this graph shows a function. Hence this graph is a linear function.

This graph is decreasing graph because the value of temperature is falling as the time passes by.

Here, x - intercept is (5.5, 0)

When the graph is observed at the x - intercept it can be said that, at 5.5 hours, the temperature will fall to $0^{\circ }F$ and beyond 5.5 hours of time, the value of temperature will be negative, whereas temperature before 5.5 hours will be positive.

Also, y - intercept is (0, 40.5)

When the graph is observed at the y - intercept it can be said that, at 0 hours, the temperature will be ${40.5}^{\circ }F$ , which is also the relative extrema (maximum value) of the graph.