Question

Sandy is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 4 km/h. After two hours, the velocity of the runner is 2 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

Just make sure to plot the in part B

Answer 2

Answer:

As per the statement: Sandy is observing the velocity of a runner at different times.

Also, after one hour, the velocity of the runner is 4 km/h. and after two hours, the velocity of the runner is 2 km/h..

(A)

Let x represents the time in hours and y represents the velocity of the runner(in km/hr)

Then, we have two points from the given statement:

(1, 4) and (2, 2)

An equation of line for two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by;

$y-y_1 = \frac{y_2-y_1}{x_2-x_1}(x-x_1)$

For the given two points (1, 4) and (2, 2) we have an equation:

$y-4 = \frac{2-4}{2-1}(x-1)$

$y-4 = \frac{-2}{1}(x-1)$

or

$y-4 = -2(x-1)$

Using distributive property: $a\cdot(b+c) = a\cdot b+ a\cdot c$

$y-4 = -2x + 2$

Add 4 on both sides we get;

$y-4 +4= -2x + 2+4$

Simplify:

$y= -2x + 6$

Add 2x on both sides we get;

$y + 2x=-2x+6+ 2x$

Simplify:

$y + 2x = 6$

[Since, standard form for linear equations in two variables is Ax+By=C]

Therefore, an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times is:

$2x+y= 6$ ; where x represents the time in hours and y represents the velocity of the runner.

(B)

Equation in part A

It is given as;  $2x+y= 6$          .....[1]

To graph this equation; for the first 4 hours.

x                  y = -2x+6

1                  4

2                 2

3                 0

4                 -2

Now, using these points (1, 4) , (2, 2) , (3, 0) and (4, -2) plot the graph as shown below in the attachment.