Problem of the Day
James borrowed money from his father to buy a used car. He is
paying his father back $40 per month until the loan is paid back.
The function that models this situation is m(x) = -40x + 800.
What is the y-intercept, and what does it represent in this
situation? What is the slope, and what does it represent in this
situation? Is this a linear function? Why or why not?

Respuesta :

Answer:

  • The y-intercept is 800 and represents the initial amount of money borrowed ($800).
  • The slope is -40 and represents the rate at which James is paying back the loan per month ($40 per month).
  • The function is linear because it is a first-degree polynomial with a constant rate of change.

Step-by-step explanation:

James borrowed money from his father to buy a used car. He is paying his father back $40 per month until the loan is paid back.

The function that models the given situation is m(x) = -40x + 800, where m(x) is the amount owed and x is the number of months since James borrowed the money.

The function is in slope-intercept form:

[tex]y = mx + b[/tex]

where:

  • m is the slope.
  • b is the y-intercept.

Therefore, the y-intercept of function m(x) is 800. This represents the initial amount of money borrowed, which is $800.

The slope is -40, which represents the rate at which James is paying back the loan per month. Since the slope is -40, it means he is reducing the amount owed by $40 per month.

The function m(x) = -40x + 800 is linear because it is a first-degree polynomial with a constant rate of change.

msm555

Answer:

Y-intercept: [tex] (0, 800) [/tex] represents the initial loan amount.

Slope: -40 represents the rate at which James pays back the loan each month.

Linearity: Yes, it is a linear function because it follows the form [tex] y = mx + b [/tex].

Step-by-step explanation:

Let's analyze the given function [tex] m(x) = -40x + 800 [/tex]:

1. Y-intercept:

  • The y-intercept occurs when [tex] x = 0 [/tex]. Substitute [tex] x = 0 [/tex] into the function:

[tex] m(0) = -40 \times 0 + 800 = 800 [/tex]

  • The y-intercept is [tex] (0, 800) [/tex].

In this context, it represents the initial amount of money borrowed by James, which is $800.

2. Slope:

  • The coefficient of [tex] x [/tex] in the function is -40.

The slope is -40.

- In this context, the slope represents the rate at which James is paying back the loan each month. It's $40, but with a negative sign indicating that he is reducing the amount owed.

3. Linearity:

Yes, this is a linear function because it is of the form:

[tex] y = mx + b [/tex],

where

  • [tex] m [/tex] is the slope and
  • [tex] b [/tex] is the y-intercept.

The function describes a straight line on a graph, and the variables are only raised to the first power.

In summary:

Y-intercept: [tex] (0, 800) [/tex] represents the initial loan amount.

Slope: -40 represents the rate at which James pays back the loan each month.

Linearity: Yes, it is a linear function because it follows the form [tex] y = mx + b [/tex].