TEKS 8.4C Worksheets — Grade 8 Use data from a table or graph

Adriana is selling lemonade at the State Fair of Texas. She sells her lemonade for $2.50 per cup. One day, she sells 12 cups and learns that her expenses, including ingredients and supplies, are $10.00. What is the slope of the line that represents her profit as a function of the number of cups sold, and what is her y-intercept if we consider her profit when no cups are sold?

1. 2.50, -10 ✓
2. 2.50, 10
3. 10, -2.50
4. 10, 2.50

Why: To find the slope, we calculate the profit per cup sold, which is $2.50. The y-intercept represents the total expenses when no cups are sold, which is $10, so the y-intercept is -10 (expenses are subtracted from profit). The slope is 2.50 and the y-intercept is -10, so the correct choice is 2.50, -10.

Sanaa is raising money for her school’s participation in the San Antonio Stock Show. She plans to sell bags of homemade cookies. The table below shows the number of bags sold and the total amount of money earned in dollars. Use the data from the table to determine the slope and y-intercept of the situation. How much money does Sanaa earn for each bag of cookies she sells? | Bags Sold | Total Earnings ($) | | --------- | ------------------ | | 5 | 15 | | 10 | 30 | | 15 | 45 | What is the slope and the y-intercept when representing this situation mathematically?

1. 3, 0 ✓
2. 3, 15
3. 15, 3
4. 0, 3

Why: To find the slope, we can use any two points from the table. For example, using the points (5, 15) and (10, 30), the slope (m) is calculated as (30 - 15) / (10 - 5) = 15 / 5 = 3. This means Sanaa earns $3 for each bag of cookies sold. The y-intercept is the total earnings when 0 bags are sold, which is $0. Thus, the slope is 3 and the y-intercept is 0.

In a recent survey at Oakwood Middle School, 80 students were asked about their favorite fruit. The results were as follows: 24 students chose apples, 32 students chose bananas, and 24 students chose oranges. What percentage of students preferred bananas?

1. 40% ✓
2. 30%
3. 35%
4. 45%

Why: To find the percentage of students who preferred bananas, divide the number of students who chose bananas (32) by the total number of students surveyed (80) and then multiply by 100. So, (32 / 80) * 100 = 40%. Therefore, the correct answer is 40%.

Zoe enjoys learning about the citrus industry in South Texas. She collects data on the height of a grapefruit tree in her backyard over a 5-month period. The tree was 2.5 feet tall at the start of the observation and grew to 5 feet tall by the end of the 5 months. Use the data to find the slope of the tree's height over time and the y-intercept representing the initial height of the tree. What is the slope of the line representing the height of the tree in feet per month?

1. 0.5 ✓
2. 1.0
3. 2.5
4. 3.0

Why: To determine the slope of the height of the grapefruit tree, we first calculate the change in height over the change in time. The tree grew from 2.5 feet to 5 feet, so the change in height is 5 - 2.5 = 2.5 feet. The change in time is 5 months. Thus, the slope is 2.5 feet / 5 months = 0.5 feet per month. Therefore, the correct answer is 0.5.

Imani is planning a road trip across Texas with her family. They will drive a total distance of 300 miles. If they travel at an average speed of 60 miles per hour, how long will the trip take in hours?

1. 5 ✓
2. 4
3. 6
4. 3

Why: To find out how long the trip will take, you can divide the total distance by the average speed. So, 300 miles ÷ 60 miles per hour = 5 hours. Therefore, the correct answer is 5.

Lucia is researching the population growth of mesquite trees in Texas. She found that in a particular area, the number of mesquite trees can be modeled by the equation y = 2x + 10, where y is the total number of trees and x is the number of years since 2020. What does the slope of this equation represent in the context of this problem?

1. The initial number of mesquite trees in 2020
2. The rate at which the number of mesquite trees increases per year ✓
3. The total number of mesquite trees after 10 years
4. The decrease in the number of mesquite trees each year

Why: The slope in the equation y = 2x + 10 is 2, which indicates that the number of mesquite trees increases by 2 trees each year. Therefore, the slope represents the rate at which the number of mesquite trees increases per year.

Tatiana is organizing a fundraiser for her school and plans to sell homemade cookies. If she sells each box of cookies for $5 and expects to sell 40 boxes, how much money will she raise if all the boxes are sold?

1. $200 ✓
2. $150
3. $250
4. $180

Why: To find the total amount Tatiana will raise, multiply the price per box by the number of boxes sold: $5 * 40 = $200. Thus, if all the boxes are sold, Tatiana will raise $200.

Thuy is studying the changes in the population of red-tailed hawks in Palo Duro Canyon over several years. In 2015, there were 120 hawks, and in 2019, the population increased to 180 hawks. What is the rate of change (slope) of the hawk population per year, and what was the initial population (y-intercept) in the year 2015?

1. 15 hawks per year; 120 hawks ✓
2. 30 hawks per year; 120 hawks
3. 15 hawks per year; 100 hawks
4. 30 hawks per year; 100 hawks

Why: To find the rate of change (slope) of the hawk population, calculate the increase in population over the number of years. From 2015 to 2019, the population increased from 120 to 180 hawks, which is an increase of 60 hawks over 4 years. The slope is 60 hawks / 4 years = 15 hawks per year. The initial population in 2015 was 120 hawks. Therefore, the correct answer is '15 hawks per year; 120 hawks'.