Respuesta :
Using a linear function, it is found that it will cost $14 to deliver 9 meals.
------------------------------
A linear function has the following format:
[tex]y = mx + b[/tex]
In which
- m is the slope(rate of change).
- b is the y-intercept(value of y when x = 0).
------------------------------
- To build the linear function, we use the two points given by the exercise: (3,10), (12,16)
------------------------------
The slope is given by the change in y divided by the change in x, thus:
- Change in y: 16 - 10 = 6
- Change in x: 12 - 3 = 9
- Slope: [tex]m = \frac{6}{9} = \frac{2}{3}[/tex]
Thus:
[tex]y = \frac{2}{3}x + b[/tex]
------------------------------
- Using one of the point, we can find b.
- I am going to use (3,10), which means that when [tex]x = 3, y = 10[/tex]. Thus:
[tex]y = \frac{2}{3}x + b[/tex]
[tex]10 = \frac{2}{3}(3) + b[/tex]
[tex]2 + b = 10[/tex]
[tex]b = 8[/tex]
The cost of delivering x meals is given by:
[tex]y = \frac{2}{3}x + 8[/tex]
------------------------------
The cost of delivering 9 meals is y when x = 9, thus:
[tex]y = \frac{2}{3}(9) + 8 = 2\times3 + 8 = 6 + 8 = 14[/tex]
It will cost $14 to deliver 9 meals.
A similar problem is given at https://brainly.com/question/21010520
