Question

modeling real life a dentist charges a flat fee for an office visit, plus an additional fee for every tooth removed. the graph shows the total cost, y (in dollars), for a patient when the dentist removes x teeth. oral surgery cost (dollars) 1000 800 600 400 200 0 (4, 900) (2, 500) 0 1 2 3 4 5 number of teeth removed interpret the slope and the y - intercept. the slope of represents the additional fee per tooth removal. the y - intercept of represents the initial fee for an office visit.

Explanation:

Step1: Calculate the slope

The formula for slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \((2, 500)\) and \((4, 900)\), we have \( m=\frac{900 - 500}{4 - 2}=\frac{400}{2} = 200 \). So the slope is 200, which represents the additional cost per tooth (since for each extra tooth, cost increases by 200).

Step2: Find the y - intercept

We use the slope - intercept form \( y=mx + b \), where \( m = 200 \). Using the point \((2, 500)\), substitute into the equation: \( 500=200\times2 + b \). Solve for \( b \): \( 500 = 400 + b\), so \( b = 100 \). The y - intercept (\( b = 100 \)) is the cost when \( x = 0 \) (no teeth removed), so it's the initial office visit fee.

Answer:

The slope is 200, and the y - intercept is 100. The slope of 200 represents the additional fee per tooth removal. The y - intercept of 100 represents the initial fee for an office visit.