Question

the data in the following table can be used to predict the number of drinks required for a person of a specified weight to be considered legally intoxicated. use the data in the table to draw a graph and to estimate the number of drinks that a 140-lb person would consume in order to be considered intoxicated. then predict the number of drinks a 240-lb person would be one drink). (the small-sized drink of any alcoholic beverage is considered to input, body weight (in pounds) 120 160 180 220 output, number of drinks 3 4 4.5 5.5 a 140-lb person can consume drink(s) in order to be considered intoxicated. (type an integer or a decimal)

Explanation:

Step1: Identify the relationship

We have a table with body weights (input) and number of drinks (output):

• Weight = 120 lb, Drinks = 3
• Weight = 160 lb, Drinks = 4
• Weight = 180 lb, Drinks = 4.5
• Weight = 220 lb, Drinks = 5.5

We can assume a linear relationship between weight (x) and number of drinks (y). Let's find the slope first.

Take two points, say (120, 3) and (160, 4). The slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 3}{160 - 120} = \frac{1}{40} = 0.025 \).

Step2: Find the equation

Using point - slope form \( y - y_1 = m(x - x_1) \), with \( (x_1,y_1)=(120,3) \) and \( m = 0.025 \):

\( y - 3=0.025(x - 120) \)

\( y=0.025x - 3+3 \)

\( y = 0.025x \)

Step3: Predict for 140 - lb person

Substitute \( x = 140 \) into the equation \( y = 0.025x \):

\( y=0.025\times140 = 3.5 \)

Answer:

3.5