At the deli counter in the supermarket, Nigel paid $10 for 2 1/2 pounds of roast beef. The cost of deli meat is proportional to its weight. What is the equation for the graph of this proportional relationship?(1 point)
The correct graph that shows the relationship between the cost for using the internet and the time it's used is:
A graph with the x-axis ranging from 0 to 6 in increments of 2 and the y-axis ranging from 0 to 3 in increments of 1 shows a line ending with an arrow. The line passes through the plotted points (0, 0), (2, 1), (4, 2), and (6, 3).
To determine the age of a dog if a human is 3 years old, we can use the proportional relationship shown in the graph.
We are given that the line passes through the point (3,21), which means that when a human is 3 years old, the corresponding dog's age is 21.
Since the age of a dog is proportional to the age of a human, we can set up a proportion to find the age of the dog:
3 (human age) / 21 (dog age) = 3 (given human age) / x (unknown dog age)
Cross multiplying, we get:
3 * x = 21 * 3
x = 21
Therefore, a 3-year-old human is the same as a 21-year-old dog.
To identify another point on the graph given the coordinate (12, 1), we need to find a point that satisfies the direct proportional relationship between the amount of water and the number of cups of rice.
By using the given coordinate (12, 1), we can write the proportion:
previous number of cups of rice / previous amount of water = new number of cups of rice / new amount of water.
Substituting the values:
1 / 12 = new number of cups of rice / new amount of water.
We can choose a new number of cups of rice and solve for the corresponding new amount of water.
From the given choices, the only option that satisfies the proportion is:
(2, 6), which means that when there are 6 cups of rice, the amount of water is 2.
Therefore, another point on the graph that satisfies the proportional relationship is (2, 6)
Let's assume that the cost of deli meat is x and the weight is y.
We are given that Nigel paid $10 for 2 1/2 pounds of roast beef, which means that the cost is 10 and the weight is 2.5.
Since the cost of deli meat is proportional to its weight, we can write the equation as:
x/y = 10/2.5
Simplifying this equation:
x/y = 4
Cross multiplying:
x = 4y
Therefore, the equation for the graph of this proportional relationship is x = 4y.
Graph Proportional Relationships Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
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Question
Use the image to answer the question.
At the Custard Creamery, the cost of ice cream custard is directly proportional to its weight in ounces. Complete the equation of the graph with its constant of proportionality.
(1 point)
$$y = x
Check Answer
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Use the image to answer the question.
A graph shows the x-axis representing weight in ounces ranging from 0 to 6 in increments of 2, and the y-axis representing cost in dollars ranging from 0 to 15 in increments of 5. A line is drawn ending with an arrow. The line begins at the origin and passes through left parenthesis 2 comma 10 right parenthesis.
At the Custard Creamery, the cost of ice cream custard is directly proportional to its weight in ounces. Complete the equation of the graph with its constant of proportionality.
(1 point)
$$
Since the cost of ice cream custard is directly proportional to its weight in ounces, we can use the two given points on the graph to find the constant of proportionality.
The two given points are (0,0) and (2,10).
We can use the formula for the slope of a line (m):
m = (y2 - y1) / (x2 - x1)
Substituting the values, we get:
m = (10 - 0) / (2 - 0) = 10 / 2 = 5
The constant of proportionality (k) is equal to the slope of the line. Therefore, the equation for the graph is:
y = 5x
Use the image to answer the question.
A graph shows the x-axis representing age of human in years ranging from 0 to 8 in increments of 1, and the y-axis representing age of dog in years ranging from 0 to 24 in increments of 3. A line is drawn. The line begins at the origin and passes through left parenthesis 3 comma 21 right parenthesis.
The age of a dog is proportional to the age of a human. Based on the graph, determine a dog’s age if a human is 3 years old.
(1 point)
A 3-year-old human is the same as a
-year-old dog.
Use the image to answer the question.
A line graph shows gasoline in gallons on the x-axis and cost in dollars on the y-axis. The x-axis ranges from 0 to 16 in increments of 2. The y-axis ranges from 0 to 40 in increments of 5. A line starts at the origin and passes through plotted point X at left parenthesis 9.375 comma 30 right parenthesis.
Trisha’s mom asked her to fill up the car’s gas tank and gave her $30 . The graph shows the total cost of gas based on the number of gallons. The point X shows the number of gallons of gasoline Trisha can purchase. State, to the nearest whole, the number of gallons of gasoline she can purchase.
(1 point)
gallons
To determine the number of gallons of gasoline Trisha can purchase with $30, we need to look at the plotted point (9.375, 30) on the graph.
Based on the x-axis representing gallons of gasoline, we can determine that Trisha can purchase approximately 9 gallons of gasoline.
Therefore, the number of gallons of gasoline she can purchase, to the nearest whole number, is 9 gallons.
Use the image to answer the question.
A line graph shows time in weeks on the x-axis and total in dollars on the y-axis. The x-axis ranges from 0 to 8 in increments of 1. The y-axis ranges from 0 to 160 in increments of 20. A line starts at the origin and passes through plotted points left parenthesis 2 comma 50 right parenthesis; left parenthesis 3 comma 75 right parenthesis; and left parenthesis 4 comma 100 right parenthesis.
Miley is saving for a new pair of boots. They cost $150 . Every week, she puts $25 into her savings account. Based on the graph, state the number of weeks it will take for her to save enough money to buy the boots.
(1 point)
weeks
To determine the number of weeks it will take for Miley to save enough money to buy the boots, we need to find the point on the graph where the total amount of dollars reaches or exceeds $150.
From the graph, we can see that the line passes through the points (2, 50), (3, 75), and (4, 100).
To identify the number of weeks it will take for Miley to save enough money, we need to find the x-coordinate (number of weeks) when the y-coordinate (total in dollars) is equal to or greater than $150.
From the given data points, we can see that Miley needs to save for at least 4 weeks to reach $100. However, this is still less than the desired amount of $150.
Since Miley saves $25 every week, we can determine that she will reach $150 in:
4 weeks + (150 - 100) / 25 = 4 weeks + 50 / 25 = 4 weeks + 2 weeks = 6 weeks
Therefore, it will take Miley 6 weeks to save enough money to buy the boots.
At the coffee shop, the cost for using the internet is proportional to the time it’s used. It costs $2 per hour to use the internet. Select the graph drawn to show this relationship, where x represents the number of hours and y represents the cost.(1 point)
Responses
A graph with the x-axis ranging from 0 to 4 in increments of 1 and the y-axis ranging from 0 to negative 4 in unit decrements shows a line ending with an arrow. The line begins at the origin and passes through three plotted points. The plotted points include left parenthesis 0 comma 0 right parenthesis; left parenthesis 1 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 4 right parenthesis.
Image with alt text: A graph with the x-axis ranging from 0 to 4 in increments of 1 and the y-axis ranging from 0 to negative 4 in unit decrements shows a line ending with an arrow. The line begins at the origin and passes through three plotted points. The plotted points include left parenthesis 0 comma 0 right parenthesis; left parenthesis 1 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 4 right parenthesis.
A graph with the x-axis ranging from 0 to 6 in increments of 2 and the y-axis ranging from 0 to 3 in increments of 1 shows a line ending with an arrow. The line passes through the plotted points left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 1 right parenthesis; left parenthesis 4 comma 2 right parenthesis; and left parenthesis 6 comma 3 right parenthesis.
Image with alt text: A graph with the x-axis ranging from 0 to 6 in increments of 2 and the y-axis ranging from 0 to 3 in increments of 1 shows a line ending with an arrow. The line passes through the plotted points left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 1 right parenthesis; left parenthesis 4 comma 2 right parenthesis; and left parenthesis 6 comma 3 right parenthesis.
A graph with the x-axis ranging from 0 to 4 in increments of 1 and the y-axis ranging from 0 to 4 in increments of 1 shows a line ending with an arrow. The line passes through 3 plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 1 comma 2 right parenthesis; and left parenthesis 2 comma 4 right parenthesis.
Image with alt text: A graph with the x-axis ranging from 0 to 4 in increments of 1 and the y-axis ranging from 0 to 4 in increments of 1 shows a line ending with an arrow. The line passes through 3 plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 1 comma 2 right parenthesis; and left parenthesis 2 comma 4 right parenthesis.
A graph with the x-axis ranging from 0 to 6 in increments of 2 and the y-axis ranging from 0 to negative 3 in unit decrements shows a line ending with an arrow. The line begins at the origin and passes through three plotted points. The plotted points include left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma negative 1 right parenthesis; and left parenthesis 4 comma negative 2 right parenthesis.
Image with alt text: A graph with the x-axis ranging from 0 to 6 in increments of 2 and the y-axis ranging from 0 to negative 3 in unit decrements shows a line ending with an arrow. The line begins at the origin and passes through three plotted points. The plotted points include left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma negative 1 right parenthesis; and left parenthesis 4 comma negative 2 right parenthesis.
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1-2-3 0r 4
The correct answer is 2.
The amount of water is directly proportional to the number of cups of rice. The coordinate (12, 1) is on the graph of this proportional relationship. Identify another point on the graph.(1 point)
Responses
(23, 4)
Left Parenthesis Start Fraction 2 over 3 End Fraction comma 4 Right Parenthesis
(2, 6)
Left Parenthesis 2 comma 6 Right Parenthesis
(14, 2)
Left Parenthesis Start Fraction 1 over 4 End Fraction comma 2 Right Parenthesis
(32, 3)
Left Parenthesis Start Fraction 3 over 2 End Fraction comma 3 Right Parenthesis
Use the image to answer the question.
A line graph titled 5 Kilometer Run shows time in minutes on the x-axis and distance in kilometers on the y-axis. The graph shows the trend for four participants: Bella, Ruby, Greg, and Paul. The x-axis ranges from 0 to 60 in increments of 10. The y-axis ranges from 0 to 15 in increments of 2.5. A line labeled Bella starts at the origin and passes through plotted point left parenthesis 45 comma 3.5 right parenthesis. A line labeled Ruby starts at the origin and passes through plotted point left parenthesis 40 comma 2.5 right parenthesis. A line labeled Greg starts at the origin and passes through plotted point left parenthesis 45 comma 2.5 right parenthesis. A line labeled Paul starts at the origin and passes through plotted point left parenthesis 25 comma 1 right parenthesis.
Four friends ran a 5K to raise money for their school. The graph shows their rates as a ratio of distance measured in kilometers and time in minutes. Based on the points shown, name the person who ran 212 km in 45 minutes.
(1 point)
Responses
Bella
Bella
Greg
Greg
Ruby
Ruby
Paul
Paul
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Based on the points shown on the graph, the person who ran 2.12 km in 45 minutes would be Bella.
Bella's line on the graph passes through the plotted point (45, 3.5), which means that after 45 minutes, Bella had run a distance of 3.5 km.
Since the question asks for the person who ran 2.12 km, which is equivalent to 212 km, in 45 minutes, the answer would be Bella.
Jayson went to the market. He bought 112 pounds of salami for $3.75. Identify the graph that shows this relationship. (1 point)
Responses
A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 1.5 comma 3.75 right parenthesis.
Image with alt text: A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 1.5 comma 3.75 right parenthesis.
A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 1.5 comma 3 right parenthesis.
Image with alt text: A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 1.5 comma 3 right parenthesis.
A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 2 comma 3.75 right parenthesis.
Image with alt text: A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 2 comma 3.75 right parenthesis.
A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 3.75 comma 1.5 right parenthesis.
Image with alt text: A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 3.75 comma 1.5 right parenthesis.
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Based on the information given, the graph that shows the relationship between the amount of salami in pounds and the cost in dollars for Jayson's purchase of 112 pounds of salami for $3.75 is:
A line graph that shows the amount in pounds on the x-axis and cost in dollars on the y-axis. The x-axis and the y-axis both range from 0 to 4 in increments of 0.25. The line starts at the origin (0,0) and passes through the plotted point (2, 3.75).
1-2-3-4
The correct
which abnswer bot Jayson went to the market. He bought 112 pounds of salami for $3.75. Identify the graph that shows this relationship. (1 point)
Responses
A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 1.5 comma 3.75 right parenthesis.
Image with alt text: A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 1.5 comma 3.75 right parenthesis.
A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 1.5 comma 3 right parenthesis.
Image with alt text: A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 1.5 comma 3 right parenthesis.
A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 2 comma 3.75 right parenthesis.
Image with alt text: A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 2 comma 3.75 right parenthesis.
A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 3.75 comma 1.5 right parenthesis.
Image with alt text: A line graph shows amount in pounds on the x-axis and cost in dollars on the y-axis. Both the x-axis and y-axis range from 0 to 4 in increments of 0.25, and are marked at 1, 2, 3 and 4. A line starts at the origin and passes through plotted point left parenthesis 3.75 comma 1.5 right parenthesis.
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Since the cost of ice cream custard is directly proportional to its weight in ounces, the equation for the graph will be in the form of y = kx, where k is the constant of proportionality.
However, without the image and any specific information about the constant of proportionality, it is not possible to complete the equation of the graph.