Thank you for visiting Find a relationship between Celsius and Fahrenheit degrees described in a linear equation given the following conditions 35 Celsius degrees correspond to 50 Fahrenheit degrees. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
The relationship between Celsius and Fahrenheit degrees can be described by a linear equation, which in this case is y = 0.4x + 36, indicating that a rise of 1 degree Celsius corresponds to a rise of 0.4 degrees Fahrenheit.
Explanation:
To find a relationship between Celsius and Fahrenheit degrees described in a linear equation, we have two pair of values: (35 ℃, 50 ℉) and (30 ℃, 48 ℉). Let's denote Celsius temperature as x and Fahrenheit temperature as y. The slope (m) of this linear equation can be found using the formula m = (y2 - y1) / (x2 - x1).
Plugging our values into this formula, we get:
m = (50 - 48) / (35 - 30) = 2 / 5 = 0.4
This tells us that for every 1 degree of rise in Celsius, Fahrenheit rises by 0.4 degrees. Now we need to find the y-intercept (b), which is the point where the line crosses the y-axis. This is found by using one of the points in the equation y = mx + b. Let's use (30, 48):
48 = 0.4(30) + b
48 = 12 + b
b = 36
Now, we can write down the final linear equation that converts Celsius to Fahrenheit: y = 0.4x + 36.
This equation tells us that a temperature in Celsius can be converted to Fahrenheit by multiplying the Celsius temperature by 0.4 and then adding 36.
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