Question

Maggie and Emma race each other along a straight running track. Maggie starts some distance ahead of Emma. The graph describes the race. What is an appropriate domain for Emma line?

Answer 1

`x \geq 0`

Explanation:

See attachment for graph

Required

Determine the domain of Emma's line

First, we calculate the equation of Emma's line

Start by calculating the slope (m)

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

Where the x's and y's represent corresponding values of x and y on Emma's line

Emma's line is represented by the thick line.

So, we have:

`(x_1,y_1) = (0,0)`

`(x_2,y_2) = (14,70)`

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

`m = (0 - 70)/(0 - 14)`

`m = (- 70)/(- 14)`

`m = (70)/(14)`

`m = 5`

The equation is then calculated using:

`y - y_1 = m(x - x_1)`

Where

`m = 5`

`(x_1,y_1) = (0,0)`

So:

`y - y_1 = m(x - x_1)`

`y - 0 = 5(x - 0)`

`y - 0 = 5x - 0`

`y = 5x`

To get the domain, we have the following:

x represents time and x can not be negative.

So, the least value of x is: x = 0

The maximum value of x is unknown.

So, the maximum value of x is: x = +infinity

Hence, the domain is

`x \geq 0`