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A camp program charges a registration fee and a daily amount.

The total bill for 12 days is $338. The total bill for 19 days is

$506. Slope can be represented by cost per day. Use x as the

number of days and y as the total cost to represent this

situation.

a. Find the slope for this situation. What does it represent?

b. Write a linear equation that models this situation.

Respuesta :

Using the information given, it is found that:

  • a) The slope is of 24, which means that for each day, the total bill increases by $24.
  • b) The linear equation is: [tex]y = 24x + 50[/tex]

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.

Item a:

  • The total bill for 12 days is $338.
  • The total bill for 19 days is  $506.

The slope is given by the change in y(total bill) divided by the change in x(number of days), hence:

[tex]m = \frac{506 - 338}{19 - 12} = 24[/tex]

The slope is of 24, which means that for each day, the total bill increases by $24.

Item b:

  • The total bill for 12 days is $338, hence, when [tex]x = 12, y = 338[/tex], and this is used to find b.

[tex]y = 24x + b[/tex]

[tex]338 = 24(12) + b[/tex]

[tex]b = 50[/tex]

Hence, the linear equation is: [tex]y = 24x + 50[/tex]

You can learn more about linear functions at https://brainly.com/question/25823744