The table that follows shows the relationship between the boiling temperature of water (°F) and the altitude (per thousand feet):
Boiling Point of Water
Altitude
(1000 ft.) Temperature
(°F)
8 197.6
4.5 203.9
3 206.6
2.5 207.5
Gemma and Tessa need to find the rate of change for the data in the previous table. A. Gemma’s first steps are +6.3/-3.5 Which two ordered pairs did Gemma use to set up her
Tessa’s first steps are +0.9/-0.5 Which two ordered pairs did Tessa use to set up her ratio?
Gemma: the first and second ordered pairs
Tessa: the third and fourth ordered pairs
I think you can observe them easily.
hope this helps :3
Yeah, I don't get this :/
To find the rate of change for the data in the table, both Gemma and Tessa need to calculate the slope between two points. The slope is determined by finding the difference in the y-values (temperatures) and dividing it by the difference in the x-values (altitude).
A. Gemma's first steps are +6.3/-3.5:
To find Gemma's ratio (+6.3/-3.5), she must choose two ordered pairs from the table. Let's denote the altitude as x and the temperature as y. Gemma wants to calculate the slope using the formula:
slope = (change in y) / (change in x)
Since Gemma's ratio is positive (+6.3), we know that the temperature is increasing as the altitude increases. Therefore, she needs to choose two points where the temperature increases. One possible choice is (4.5, 203.9) as the first point and (3, 206.6) as the second point.
The calculation for Gemma's ratio will be:
slope = (change in y) / (change in x) = (206.6 - 203.9) / (3 - 4.5) = 2.7 / (-1.5) = -1.8
However, Gemma's ratio is not -1.8 but +6.3. Therefore, there must be an error in the question or the data provided. It seems like the given ratio does not match the data.
Tessa's first steps are +0.9/-0.5:
Similarly, Tessa needs to choose two ordered pairs to calculate her ratio (+0.9/-0.5). Since her ratio is positive (+0.9), she also wants to choose two points where the temperature increases. One possible choice is (3, 206.6) as the first point, and (2.5, 207.5) as the second point.
The calculation for Tessa's ratio will be:
slope = (change in y) / (change in x) = (207.5 - 206.6) / (2.5 - 3) = 0.9 / (-0.5) = -1.8
Here, Tessa's ratio does match the given ratio (+0.9/-0.5). Therefore, the two ordered pairs Tessa used to set up her ratio are (3, 206.6) and (2.5, 207.5).