Ratios in the Coordinate Plane Quick Check
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Question
Use the image to answer the question.
A coordinate plane shows red paint on the X-axis and blue paint on the Y-axis. The X-axis ranges from 0 to 10 in increments of 2. The Y-axis ranges from 0 to 15 in increments of 3. The data points are left parenthesis 2 comma 3 right parenthesis, left parenthesis 4 comma 6 right parenthesis, left parenthesis 6 comma 9 right parenthesis, and left parenthesis 8 comma 12 right parenthesis.
What is the ratio of red paint to blue paint?
(1 point)
Responses
1:3
ratio of 1 to 3
2:3
ratio of 2 to 3
1:2
ratio of 1 to 2
3:4
ratio of 3 to 4
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To find the ratio of red paint to blue paint, we need to determine the total amount of red and blue paint used.
Looking at the data points, we can see that for every increment of 2 on the X-axis (red paint), there is a corresponding increment of 3 on the Y-axis (blue paint).
Therefore, the ratio of red paint to blue paint is 2:3.
Use the image to answer the question.
A coordinate plane shows an x-axis ranging from 0 to 5 in increments of 1 and a y-axis ranging from 0 to 20 in increments of 4. The data points are left parenthesis 2 comma 8 right parenthesis, left parenthesis 3 comma 12 right parenthesis, left parenthesis 4 comma 16 right parenthesis, and left parenthesis 5 comma 20 right parenthesis.
Choose the coordinate pair to plot on the coordinate plane so the ratio stays equivalent.
(1 point)
Responses
(1, 3)
Left Parenthesis 1 comma 3 Right Parenthesis
(4, 1)
Left Parenthesis 4 comma 1 Right Parenthesis
(1, 4)
Left Parenthesis 1 comma 4 Right Parenthesis
(0, 4)
Left Parenthesis 0 comma 4 Right Parenthesis
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To find the ratio of red paint to blue paint, we need to determine the total lengths of the X-axis (red paint) and the Y-axis (blue paint).
In this case, we are given that the X-axis ranges from 0 to 10 in increments of 2. This means that the total length of the X-axis is 10 units.
Similarly, the Y-axis ranges from 0 to 15 in increments of 3, so the total length of the Y-axis is 15 units.
Now, we need to determine the lengths of the red paint and blue paint based on the given data points. The data points given are (2,3), (4,6), (6,9), and (8,12). These points represent the x-coordinate (red paint) and y-coordinate (blue paint) respectively.
To calculate the length of the red paint, we need to look at the x-coordinates and find the difference between the smallest x-coordinate and the largest x-coordinate. In this case, the smallest x-coordinate is 2 and the largest x-coordinate is 8, so the length of the red paint is 8 - 2 = 6 units.
To calculate the length of the blue paint, we do the same with the y-coordinates. The smallest y-coordinate is 3 and the largest y-coordinate is 12, so the length of the blue paint is 12 - 3 = 9 units.
Now, we can find the ratio of red paint to blue paint by dividing the length of the red paint by the length of the blue paint:
Ratio = Length of red paint / Length of blue paint = 6 / 9
Simplifying the ratio, we get:
Ratio = 2 / 3
Therefore, the ratio of red paint to blue paint is 2:3. This option corresponds to response 2 in the given choices.
To determine a coordinate pair that maintains an equivalent ratio, we need to find a point that has the same ratio of x-axis increment to y-axis increment as the given data points.
Looking at the given data points, we can see that for every increment of 1 on the x-axis, there is a corresponding increment of 4 on the y-axis. Therefore, the ratio of x-axis increment to y-axis increment is 1:4.
To maintain an equivalent ratio, we need to find a point that has the same ratio of x-axis increment to y-axis increment, which is 1:4.
Among the given options, the coordinate pair (1, 4) has the same ratio of 1:4. Therefore, the correct answer is (1, 4).