Question
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Is the following proportional or non-proportional? If so what is the k value.
hour:2,3,4,5
temp:60,63,70,73
Question 3 options:
Proportional; k = 30
Non-proportional
Proportional; k = -30
Proportional; k = 21
Answers
GPT-4o mini
To determine if the relationship between the hours and the temperature is proportional, we need to check if there is a constant ratio \( k \) between them. A proportional relationship means that the ratio of the two variables is constant.
Let's find the ratios for each pair of values:
For hour 2 and temp 60:
\[ k = \frac{temp}{hour} = \frac{60}{2} = 30 \]
For hour 3 and temp 63:
\[ k = \frac{temp}{hour} = \frac{63}{3} = 21 \]
For hour 4 and temp 70:
\[ k = \frac{temp}{hour} = \frac{70}{4} = 17.5 \]
For hour 5 and temp 73:
\[ k = \frac{temp}{hour} = \frac{73}{5} = 14.6 \]
Since the value of \( k \) differs for each pair, we can conclude that the relationship is **non-proportional**.
So the answer is:
**Non-proportional**.
Let's find the ratios for each pair of values:
For hour 2 and temp 60:
\[ k = \frac{temp}{hour} = \frac{60}{2} = 30 \]
For hour 3 and temp 63:
\[ k = \frac{temp}{hour} = \frac{63}{3} = 21 \]
For hour 4 and temp 70:
\[ k = \frac{temp}{hour} = \frac{70}{4} = 17.5 \]
For hour 5 and temp 73:
\[ k = \frac{temp}{hour} = \frac{73}{5} = 14.6 \]
Since the value of \( k \) differs for each pair, we can conclude that the relationship is **non-proportional**.
So the answer is:
**Non-proportional**.