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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?

Sagot :

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 ⇒ rate of change
  • b is the y-intercept ⇒ initial value

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

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

→ By comparing it with the form of the linear equation above

∴ m = 40

∴ b = 30

∵ b represents the y-intercept

∴ The y-intercept is 30

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

∴ The y-intercept represents the registration fee

∵ m is the slope

∴ The slope is 40

∵ The slope represents the rate of change

∴ The slope represents the cost per lesson

∵ x represents the number of lessons

∵ The number of lessons is 6

∴ x = 6

→ Substitute x by 6 in the equation to find the total cost of 6 lessons

∵ y = 40(6) + 30

∴ y = 240 + 30

∴ y = 270

∵ y represents the total cost

∴ The total cost of 6 lessons is $270

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