Question

Which graphs show functions with direct variation? Select three options. A coordinate plane showing Parking Garage Rates with Time in hours on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2.4) and (5, 4). A coordinate plane showing Cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5). A coordinate plane showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6). A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8). A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).

Answer 1

Answer:

A coordinate plane showing Parking Garage Rates with Time in hours on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2.4) and (5, 4).

A coordinate plane showing Cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5).

A coordinate plane showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).

A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).

A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8)

Answer 2

Thus the required graphs, which show functions with a direct variation are the coordinate plane showing the cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5), and that showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).

Given:

A coordinate plane showing Parking Garage Rates with Time in hours on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2.4) and (5, 4).

A coordinate plane showing the cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5).

A coordinate plane showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).

A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).

A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).

To Find:

The graphs, which show functions with a direct variation.

Solution:

We can find the solution to this problem in the following way.

We know that the graph on the XY plane is the plotting of a function along the X-axis and the Y-axis.

We see that the graph depicting the direct variation has the property of having the same proportionality between the abscissa values and the ordinate values irrespective of the points on the XY plane.

We shall now examine the points at (1, 0.3) and (5, 1.5).

The ratio of abscissa values $=\frac{5}{1}=5$

The ratio of ordinate values $=\frac{1.5}{0.3}=5$

We find that the points (1, 0.3) and (5, 1.5) exhibit direct variation.

We shall examine the points at (1, 1.2) and (5, 6).

The ratio of abscissa values $=\frac{5}{1}=5$

The ratio of ordinate values $=\frac{6}{1.2}=5$

We find that among the given graphs only the following two graphs show the direct variation.

A coordinate plane showing the cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5).

A coordinate plane showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).

Thus the required graphs, which show functions with a direct variation are the coordinate plane showing the cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5), and that showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).

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