Question

Eric is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After three 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.

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

Answer 1

Slope intercept form: The straight line equation is given by:

`y-y_1=m(x-x_1)`, .....[1] where m is the slope of the line.

(A)

Let x represents the number of hours and y represents the velocity of the runner.

As per the statement: After one hour, the velocity of the runner is 5 km/h. After three hours, the velocity of the runner is 3 km/h.

we have two points as (1, 5) and (3, 3)

Calculate first slope.

Formula for slope(m) is given by;

`m = (y_2-y_1)/(x_2-x_1)`

Then substitute the given values we get;

`m = (3-5)/(3-1) = (-2)/(2) =-1`

Now, substitute the value of m = -1 and (1, 5) in equation [1] we have;

`y-5=-1(x-1)`

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

`y-5 = -x + 1`

Add both sides by 5 we get;

`y = -x + 6`

or

`x+ y = 6`

Therefore, an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times is,
`x+ y = 6`

(B)

x y = 6 -x

1 5

2 4

3 3

4 2

5 1

Now, plot these points on the graph for the first 5 hours as shown below in the attachment.