Question

A music school charges a registration fee in addition to a fee per lesson. Music lessons last 0.5 hour. The equation y = 40x + 30 represents the total cost y of x lessons. Find and interpret the slope and y-intercept of the line that represents this situation.

Answer 1

The slope of the equation y = 40x + 30 is 40, indicating a cost of $40 per lesson. The y-intercept is 30, which represents a registration fee at the music school.

Step-by-step explanation:

The student is asked to find and interpret the slope and y-intercept of the linear equation y = 40x + 30, which represents the total cost y of x music lessons. The slope is the coefficient of x, which in this equation is 40. This means that for each additional lesson, the cost increases by $40. This can be interpreted as the fee per lesson. The y-intercept is the constant term, which in this case is 30. This represents the registration fee that is charged regardless of the number of lessons taken, which is the total cost when x = 0.