Question

modeling real life a dentist charges a flat fee for an office visit, plus an additional fee for each patient when the dentist removes x teeth. chart: oral surgery, x-axis: number of teeth removed, y-axis: cost (dollars), points (2, 500), (4, 900), line from (0, ~100) to (5, ~1100) interpret the slope and the y-intercept. the slope of dropdown represents the additional fee per tooth removal. the y-intercept of dropdown represents the initial fee for an office visit.

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). 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, representing the additional fee per tooth removal.

Step2: Find the y - intercept

The y - intercept is the value of \( y \) when \( x = 0 \). From the graph, when \( x = 0 \), \( y=100 \) (by looking at the y - axis where the line crosses, or we can use the slope - intercept form \( y=mx + b \). Using the point \((2, 500)\) and \( m = 200 \), we substitute into \( y=mx + b \): \( 500=200\times2 + b \), \( 500 = 400 + b \), so \( b = 100 \). The y - intercept is 100, representing the initial office visit fee.

Answer:

The slope of \( 200 \) represents the additional fee per tooth removal.
The \( y \) - intercept of \( 100 \) represents the initial fee for an office visit.