Question

lesson 2 extra practice
use trend lines to make predictions

1. the table below shows attendance at an annual fourth of july concert.

year	2	3	4	5	6

a. construct a scatterplot of the data. then draw a line that best represents the data.
b. write an equation for the trend line.
c. use the equation to make a conjecture about the number of attendees in the tenth year.

1. the table shows the number of people that attended a family reunion each year.

year	1	2	3	4	5	6	7

a. construct a scatterplot of the data. then draw a line that best represents the data.
b. write an equation for the trend line.
c. use the equation to make a conjecture about the number of people that might attend the reunion in the fifteenth year.

Explanation:

Problem 1c:

Step1: Identify the equation

The trend line equation is \( y = 127.5x + 555 \).

Step2: Substitute \( x = 10 \)

Substitute \( x = 10 \) into the equation: \( y = 127.5(10) + 555 \).

Step3: Calculate the value

First, calculate \( 127.5\times10 = 1275 \). Then, add 555: \( 1275 + 555 = 1830 \).

Step1: Find the slope

Use two points, e.g., (1, 115) and (7, 145). Slope \( m=\frac{145 - 115}{7 - 1}=\frac{30}{6}=5 \).

Step2: Find the y - intercept

Use point - slope form \( y - y_1=m(x - x_1) \). Using (1, 115): \( y - 115 = 5(x - 1) \). Simplify: \( y - 115 = 5x-5 \), so \( y = 5x + 110 \).

Step1: Identify the equation

The trend line equation is \( y = 5x + 110 \).

Step2: Substitute \( x = 15 \)

Substitute \( x = 15 \) into the equation: \( y = 5(15)+110 \).

Step3: Calculate the value

First, calculate \( 5\times15 = 75 \). Then, add 110: \( 75 + 110 = 185 \).

Answer:

The number of attendees in the tenth year is 1830.

Problem 2b: