2 of 192 of 19 Items
12:39
Skip to resources
Question
Joaquin built a ramp for his little brother to use with with toy cars. The relationship between the length of the ramp, x
, and the height of the ramp, y
, are is shown in the graph.
Which statement correctly explains the meaning of the rate of change for this graph?
Responses
A The ramp has a 1-inch change in height for every 5-inch change in length. The ramp has a 1-inch change in height for every 5-inch change in length.
B The ramp has a 1-inch change in height for every 3-inch change in length. The ramp has a 1-inch change in height for every 3-inch change in length.
C The ramp has a 3-inch change in height for every 1-inch change in length. The ramp has a 3-inch change in height for every 1-inch change in length.
D The ramp has a 4-inch change in height for every 10-inch change in length.
C The ramp has a 3-inch change in height for every 1-inch change in length.
To find the correct statement explaining the meaning of the rate of change for this graph, we need to examine the slope of the graph. The slope represents the rate of change between the length and height of the ramp.
From the graph, we can see that the ramp has a rise (change in height) of 2 inches and a run (change in length) of 19 inches.
Therefore, the rate of change of the graph is 2/19 in terms of inches.
Among the given options, only option A explains this rate of change correctly. It states that the ramp has a 1-inch change in height for every 5-inch change in length. This is consistent with the calculated rate of change of 2/19, where 2/19 ≈ 1/5.
So, the correct statement is:
A) The ramp has a 1-inch change in height for every 5-inch change in length.
To determine the meaning of the rate of change for this graph, we need to look at the slope of the line on the graph. The slope represents the ratio of the change in y (height) to the change in x (length).
In this case, the line goes from (0, 0) to (19, 2). To find the slope, we can use the formula (y2 - y1)/(x2 - x1).
Substituting the coordinates, we get (2 - 0)/(19 - 0) = 2/19.
This means that for every 19-inch change in length, there is a 2-inch change in height.
Comparing this to the options given:
A) The slope mentioned here is 1/5, which is not the same as the calculated slope of 2/19.
B) The slope mentioned here is 1/3, which is not the same as the calculated slope of 2/19.
C) The slope mentioned here is 3/1, which is not the same as the calculated slope of 2/19.
D) The slope mentioned here is 4/10, which simplifies to 2/5. This is not the same as the calculated slope of 2/19.
Therefore, the correct statement explaining the meaning of the rate of change is:
The ramp has a 2-inch change in height for every 19-inch change in length.