Question

Max is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After two hours, the velocity of the runner is 3 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equations obtained in Part A for the first 4 hours? (5 points)

Answer 1

You only have two observations to work the equation for the velocity.

You only can assume a linear relation.

Part a.

Calling x the independent variable (time in hours) and y the dependent variable (velocity in km/h) =>

x (time in hours)         y (velocity in km/h)

1                                  5
2                                  3

Now you use the linear relation:

slope: (3 - 5) km/h/ (2 - 1)h = - 2 km/1h^2 = - 2 km/h ^2

Equation:

y - 3 = slope * (x - 2)

=> y - 3 = - 2 ( x - 2)

=> y - 3 = - 2x + 4

=> y = 3 - 2x + 4

=> y = - 2x + 7

that is the slope-intercept form.

the standard form is y + 2x - 7 = 0

part B.

to draw the graph you can make a table with the points for the first four hours:

x (time in hours)            y (velocity in km/h)
                                        -2x + 7

1                                      -2(1) + 7 = 5

2                                      -2(2) + 7 = 3

3                                      -2(3) + 7 = 1

4                                     -2(4) + 7 = - 1

The graph, of course, is a straight line, because we started from that assumption.