katie, mike, sharon, and bart are each mixing red an yellow paint to make different shades of orange. The graph represents the relationships pf the ratios of red to yellow parts in each paint mixture. Whose color mixture shows a proportional relationship between the number of parts of red paint and the number of parts of yellow paint?
here is the graph points.
mike; (4,9)
katie; (8,9)
bart; (9,8)
sharon; (9,9)
The color mixture that shows a proportional relationship between the number of parts of red paint and the number of parts of yellow paint is Katie's mixture.
To determine which color mixture shows a proportional relationship between the number of parts of red paint and yellow paint, we need to compare the ratios of red to yellow parts in each paint mixture.
Let's calculate the ratios for each person:
- Mike: 4 red parts, 9 yellow parts. Ratio = 4:9.
- Katie: 8 red parts, 9 yellow parts. Ratio = 8:9.
- Bart: 9 red parts, 8 yellow parts. Ratio = 9:8.
- Sharon: 9 red parts, 9 yellow parts. Ratio = 9:9, which simplifies to 1:1.
The ratios that show a proportional relationship are the ones where the ratio is the same for both mixtures. In this case, only Mike and Katie have the same ratio of red to yellow parts: 4:9 and 8:9. Therefore, both Mike and Katie's color mixtures show a proportional relationship between the number of parts of red paint and yellow paint.
To determine whose color mixture shows a proportional relationship between the number of parts of red paint and the number of parts of yellow paint, we need to examine the ratios of red to yellow parts for each person.
Let's calculate the ratios for each mixture:
- Mike: 4 parts red to 9 parts yellow (4:9)
- Katie: 8 parts red to 9 parts yellow (8:9)
- Bart: 9 parts red to 8 parts yellow (9:8)
- Sharon: 9 parts red to 9 parts yellow (9:9)
To check if the ratios are proportional, we need to compare the ratios' values. In a proportional relationship, the value of one ratio can be obtained by multiplying or dividing the other ratio by the same number.
Comparing the ratios, we find:
- Mike: 4:9
- Katie: 8:9
- Bart: 9:8
- Sharon: 9:9
Among these ratios, only Mike's ratio (4:9) and Katie's ratio (8:9) are proportional. This means that Mike's color mixture (4 parts red to 9 parts yellow) and Katie's color mixture (8 parts red to 9 parts yellow) demonstrate a proportional relationship between the number of parts of red paint and yellow paint.