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)
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Let's call the weight of the roast beef x and the cost of the roast beef y.
We know that the cost of the roast beef is proportional to its weight, so we can write the equation as y = kx, where k is the constant of proportionality.
We also know that Nigel paid $10 for 2 1/2 pounds of roast beef. The decimal form of 2 1/2 is 2.5. Plugging this into the equation, we get 10 = k(2.5).
Simplifying the equation, we get 10 = 2.5k.
To solve for k, we divide both sides of the equation by 2.5: k = 10/2.5 = 4.
Therefore, the equation for the graph of this proportional relationship is y = 4x.
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)
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Since the line passes through the point (2,10), we can use this point to find the constant of proportionality.
Let x be the weight in ounces and y be the cost in dollars.
We can use the equation y = kx, where k is the constant of proportionality.
Plugging in the values from the point (2,10), we get 10 = 2k.
To solve for k, we divide both sides of the equation by 2: k = 10/2 = 5.
Therefore, the equation for the graph of this proportional relationship 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.
To determine the age of a dog if a human is 3 years old, we can use the graph.
We can see from the graph that the line passes through the point (3, 21). This means that when a human is 3 years old, a dog is 21 years old.
Therefore, a 3-year-old human is the same as an 21-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, we can use the graph.
From the graph, we can see that the line passes through the point X which is at (9.375, 30). This means that Trisha can purchase 9.375 gallons of gasoline with $30.
Rounding to the nearest whole number, Trisha can purchase approximately 9 gallons of gasoline.
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 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.
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 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.
The correct graph to show 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 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.
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
(14, 2)
Left Parenthesis Start Fraction 1 over 4 End Fraction comma 2 Right Parenthesis
(2, 6)
Left Parenthesis 2 comma 6 Right Parenthesis
(23, 4)
Left Parenthesis Start Fraction 2 over 3 End Fraction comma 4 Right Parenthesis
(32, 3)