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.
