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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
∵ 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