Answer:
[tex]x \geq 0[/tex]
Step-by-step 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)
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
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:
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (14,70)[/tex]
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex] becomes
[tex]m = \frac{0 - 70}{0 - 14}[/tex]
[tex]m = \frac{- 70}{- 14}[/tex]
[tex]m = \frac{70}{14}[/tex]
[tex]m = 5[/tex]
The equation is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = 5[/tex]
[tex](x_1,y_1) = (0,0)[/tex]
So:
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - 0 = 5(x - 0)[/tex]
[tex]y - 0 = 5x - 0[/tex]
[tex]y = 5x[/tex]
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
[tex]x \geq 0[/tex]
