Odval is comparing the price of gas at two gas stations near her home. The gas station across the street from her (Gas Station A) is selling gas for $4.12 per gallon. Her brother tells her that he just got 5 gallons of gas from the gas station down the street (Gas Station B) for $19.95.Odval knows that for each gas station, the relationship between the number of gallons of gas and the price is a proportional relationship. She knows the unit rate at Gas Station A is $4.12 per gallon. At Gas Station B, the unit rate is $19.955=$3.99 per gallon.Odval decides to create a table and a graph to represent the proportional relationship between gallons of gas and price for each gas station.Gallons of GasPrice ($) at Gas Station APrice ($) at Gas Station B 14.123.9928.247.98312.3611.97416.4815.96520.6019.95A coordinate plane shows gallons of gas on the x-axis ranging from 0 to 6 in increments of 1. The y-axis shows price in dollars ranging from 0 to 24 in increments of 2.A solid line with an arrow at one end is labeled A and a dotted line with an arrow at one end is labeled B. The solid line extends from left parenthesis 0 comma 0 right parenthesis to approximately left parenthesis 6 comma 24.7 right parenthesis. The dotted line extends from left parenthesis 0 comma 0 right parenthesis to left parenthesis 6 comma 23.9 right parenthesis.Odval feels that both her table and graph demonstrate that Gas Station B has a better deal on gas right now.Interpret Odval’s table and graph. How do both the table and the graph show the relationship between the number of gallons of gas and the price? How did Odval demonstrate her ability to reason abstractly and quantitatively?
Both the table and the graph show a proportional relationship between the number of gallons of gas and the price at both gas stations. As the number of gallons increases, the price also increases proportionally.
In the table, each row represents a specific number of gallons of gas, and the corresponding price at each gas station is listed. The price at Gas Station A increases by $4.12 for every gallon added, while the price at Gas Station B increases by $3.99 for every gallon added. This demonstrates the proportional relationship between gallons of gas and price at each gas station.
In the graph, the x-axis represents the number of gallons of gas, and the y-axis represents the price in dollars. The solid line (labeled A) represents the relationship at Gas Station A, and the dotted line (labeled B) represents the relationship at Gas Station B. Both lines start at the origin (0,0) and increase steadily as the number of gallons increases. The slopes of the lines represent the unit rates of price change per gallon at each gas station.
Odval demonstrates her ability to reason abstractly and quantitatively by analyzing the data and making comparisons between the two gas stations. She understands the concept of unit rate and applies it to calculate the price per gallon at each gas station. She then uses this information to create a table and a graph that clearly represent the relationship between gallons of gas and price at both gas stations.
The table and graph provided by Odval show the relationship between the number of gallons of gas and the price at Gas Station A and Gas Station B.
In the table, each row represents a specific number of gallons of gas, with the corresponding prices at Gas Station A and Gas Station B. The prices increase proportionally with the number of gallons, as indicated by the unit rates for each gas station. Gas Station A has a unit rate of $4.12 per gallon, while Gas Station B has a unit rate of $3.99 per gallon.
The graph visually represents this relationship. The x-axis represents the gallons of gas, ranging from 0 to 6 in increments of 1. The y-axis represents the price in dollars, ranging from 0 to 24 in increments of 2.
The solid line labeled A represents the price at Gas Station A, starting from (0, 0) and extending to approximately (6, 24.7). The dotted line labeled B represents the price at Gas Station B, starting from (0, 0) and extending to (6, 23.9).
By comparing the prices at both gas stations in the table and graph, Odval is able to reason abstractly and quantitatively. She recognizes that Gas Station B offers a lower price per gallon of gas, as indicated by the unit rates. This demonstrates her ability to apply mathematical reasoning and analyze the data to make an informed decision.
Both the table and the graph provided by Odval show the relationship between the number of gallons of gas and the price at Gas Station A and Gas Station B.
In the table, the first column represents the number of gallons of gas, the second column represents the price in dollars at Gas Station A, and the third column represents the price in dollars at Gas Station B. Each row in the table shows the corresponding prices for a specific number of gallons of gas. By comparing the prices in each row, Odval can easily see which gas station offers a better deal for a given number of gallons.
In the graph, the x-axis represents the number of gallons of gas, ranging from 0 to 6. The y-axis represents the price in dollars, ranging from 0 to 24. The solid line labeled A represents the price at Gas Station A, and the dotted line labeled B represents the price at Gas Station B. The lines start at the origin (0, 0) and extend to the respective points on the graph, showing how the price changes as the number of gallons increases.
By analyzing both the table and the graph, Odval demonstrated her ability to reason abstractly and quantitatively. She was able to compare the prices at different gas stations by recognizing and understanding the unit rate for each gas station. She then applied her knowledge to create a table and graph that visually represent the relationship between the gallons of gas and the price at each gas station. This shows her ability to think logically and make informed decisions based on data and numerical reasoning.