Using a linear function, it is found that it takes Julia 10 minutes to get ready for a delivery.
Linear functions:
A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0.
In this problem:
- For a distance of 6 km, she takes 46 minutes.
- For a distance of 8 km, she takes 58 minutes.
- For a distance of 10 km, she takes 70 minutes.
We have that when the distance changes by 2 km, the time increases by 12 minutes, hence the slope is:
[tex]m = \frac{12}{2} = 6[/tex]
Then:
[tex]y = 6x + b[/tex]
When [tex]x = 6, y = 46[/tex], which we use to find b, which is the time it takes Julia to get ready for a delivery.
[tex]y = 6x + b[/tex]
[tex]46 = 6(6) + b[/tex]
[tex]b = 10[/tex]
It takes Julia 10 minutes to get ready for a delivery.
To learn more about linear functions, you can take a look at https://brainly.com/question/24282972
