Question

Linda is training to be an assistant at the local animal shelter. To become an assistant she needs to complete 48 h of training. Linda keeps a graph of the number of hours of training left to be completed. What is the rate of change of the number of hours remaining with respect to the number of days? Remember to include units.

Answer 1

The equation between the number of days remaining and number of hours is given as y= -5x+50.

How to illustrate the equation?

Let y be the number of days remaining and x be the no.of hours.

From the graph the slope of the line is given by m.

m=(y2 - y1)/(x2 - x1)

m=(30 - 40)/(4 - 2)

m= -10/2 = -5.

The above slope is in between points 2 and 4. As the line has a constant rate of growth the slope is the same between any points of the line.

Therefore the equation between the no.of days remaining and no.of hours is given by

y=mx +c.

y=-5x+c

Now to find the value of c. This can be determined by substituting the x and y values at a particular instant. For x=0,y=50. Therefore by these values, we get,

50= -5(0)+c

c=50.

Therefore the relation between the number of days remaining and number of hours is given as y= -5x+50.

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