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A music company offers lessons. They charge a registration fee $30 and the $40 per lesson. The equation y=40x+30 represents the total cost y of x lessons.

What is the y intercept and what does it represent in the context of the problem?

What is the slope and what does it represent in the context of the problem?

What is the total cost if 6 lessons where taken?

Respuesta :

Ashraf82

Answer:

The y-intercept is 30 and represents the registration fee

The slope is 40 and represents the cost per lesson

The total cost of 6 lessons is $270

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

  • m is the slope of the line ā‡’ rate of change
  • b is the y-intercept ā‡’ initial value

āˆµ A music company charges a registration fee of $30 and $40 per lesson

āˆµ The equation y = 40x + 30 represents the total cost y of x lessons

ā†’ By comparing it with the form of the linear equation above

āˆ“ m = 40

āˆ“ b = 30

āˆµ b represents the y-intercept

āˆ“ The y-intercept is 30

āˆµ The y-intercept is the initial value (value y at x = 0)

āˆ“ The y-intercept represents the registration fee

āˆµ m is the slope

āˆ“ The slope is 40

āˆµ The slope represents the rate of change

āˆ“ The slope represents the cost per lesson

āˆµ x represents the number of lessons

āˆµ The number of lessons is 6

āˆ“ x = 6

ā†’ Substitute x by 6 in the equation to find the total cost of 6 lessons

āˆµ y = 40(6) + 30

āˆ“ y = 240 + 30

āˆ“ y = 270

āˆµ y represents the total cost

āˆ“ The total cost of 6 lessons is $270