Slope as Unit Rate Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.
An illustration shows two graphs depicting cost of gasoline per gallon in dollars in store A and B. The first graph shows cost of gasoline per gallon in dollars in store A. The horizontal axis shows gallons ranging from 0 to 20 in increments of 5. The vertical axis shows the cost in dollars ranging from 0 to 70 in increments of 10. Four data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 5 comma 20 right parenthesis, left parenthesis 10 comma 40 right parenthesis, and left parenthesis 15 comma 60 right parenthesis. A line connects all the data points. The second graph shows cost of gasoline per gallon in dollars in store B. The horizontal axis shows gallons ranging from 0 to 10 in increments of 2. The vertical axis shows the cost in dollars ranging from 0 to 30 in increments of 2. Three data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 4 comma 14 right parenthesis, and left parenthesis 8 comma 28 right parenthesis. A line connects all the data points.
The proportional relationship between the cost of gasoline and the number of gallons of gasoline from Store A and Store B are displayed in the graphs. Use the graphs to interpret the store that has the cheaper cost of gasoline per gallon.
(1 point)
Responses
Store A has the cheaper gasoline. The cost of gasoline is $0.25 per gallon.
Store A has the cheaper gasoline. The cost of gasoline is $0.25 per gallon.
Store B has the cheaper gasoline. The cost of gasoline is $3.50 per gallon.
Store B has the cheaper gasoline. The cost of gasoline is $3.50 per gallon.
Store B has the cheaper gasoline. The cost of gasoline at Store A is $100 per gallon.
Store B has the cheaper gasoline. The cost of gasoline at Store A is $100 per gallon.
Store B has the cheaper gasoline. The cost of gasoline at Store A is $5 per gallon.
Store B has the cheaper gasoline. The cost of gasoline is $3.50 per gallon.
To determine which store has the cheaper cost of gasoline per gallon, we need to compare the slopes of the two graphs. The slope represents the rate of change or the cost per gallon.
Looking at the first graph (Store A), we can see that when the number of gallons increases by 5 (from 5 to 10), the cost increases by 20 (from 20 to 40). This means that for every 5 gallons, the cost increases by $20.
Calculating the slope for Store A:
Slope = (change in cost)/(change in gallons) = 20/5 = $4 per gallon
Now let's look at the second graph (Store B). When the number of gallons increases by 4 (from 4 to 8), the cost increases by 14 (from 14 to 28). This means that for every 4 gallons, the cost increases by $14.
Calculating the slope for Store B:
Slope = (change in cost)/(change in gallons) = 14/4 = $3.50 per gallon
Comparing the slopes of the two graphs, we can see that the slope for Store A is greater than the slope for Store B. This means that Store B has the cheaper cost of gasoline per gallon.
Therefore, the correct answer is: Store B has the cheaper gasoline. The cost of gasoline is $3.50 per gallon.
To determine which store has the cheaper cost of gasoline per gallon, we need to compare the slopes of the two lines on the graphs.
First, let's analyze the graph for Store A. It shows that for every 5 gallons of gasoline, the cost increases by $20. We can find the slope by calculating the change in y (cost) divided by the change in x (gallons).
The change in y is $20, and the change in x is 5 gallons. So the slope for Store A is:
Slope_A = change in y / change in x = $20 / 5 gallons = $4/gallon.
Now let's analyze the graph for Store B. It shows that for every 4 gallons of gasoline, the cost increases by $14. Again, calculating the slope:
The change in y is $14, and the change in x is 4 gallons. So the slope for Store B is:
Slope_B = change in y / change in x = $14 / 4 gallons = $3.50/gallon.
Comparing the slopes, we can see that Store A has a slope of $4/gallon, while Store B has a slope of $3.50/gallon.
Since Store B has a lower slope (or rate), it means that the cost of gasoline is cheaper at Store B.
Therefore, the correct response is: Store B has the cheaper gasoline. The cost of gasoline is $3.50 per gallon.