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 runner 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 have velocity 1 of 5 km per hour after 1 hour and velocity 2 of 3 km per hour after 2 hours.

Part A)

Let Velocity = a +bt, with t being the time in hours.

For velocity 1 you have a +b = 5

For velocity 2, you have a + 2b =3

Now subtract velocity 1 from velocity 2:

a +2b - (a+b) = 3-5

Simplify to get b = -2

Now solve for a in the first equation:

a + b =5

Replace b with -2:

a - 2 = 5

a = 7

Now replace a and b in the original formula:

Velocity = 7 -2t

Part B)

Create a table with x and Y values to graph.

X axis would be the time and the velocity would be the Y axis

Your time would be 0 , 1, 2 3 and 4 hours.

Using the final equation from part A, replace t with the hours ans solve for the velocities, which become the y axis:

7 - 2(0) = 7-0 = 7

7 - 2(1) = 7-2 = 5

7 - 2(2) = 7-4 = 3

7 - 2(3) = 7-6 = 1

7-2(4) = 7-8 = -1

Now you have your x and y coordinates to plot on a graph:

(0,7) (1,5) (2,3) (3,1) and (4,-1)

Answer 2

• A) 2x +y = 7
• B) see the attached graph

Explanation:

Part A. Let x represent the number of hours after the runner starts; let y represent the velocity of the runner in km/h. You are given two points (x, y) = (1, 5) and (2, 3) and asked to write a standard form equation for a line through them.

It may be convenient to start with the form ...

... (y2 -y1)(x -x1) = (x2 -x1)(y -y1)

Filling in the given point values, this is ...

... (3-5)(x -1) = (2-1)(y -5)

... -2x +2 = y -5

... 2x +y = 7 . . . . . . add 5+2x to put into standard form

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Part B. You can plot the two points from Part A and draw the line through them to graph the equation of their line. You will note that the runner's velocity is predicted to be negative after 3.5 hours.