Use the following Info. At sea level the speed of sound in air is linearly related to air temp. If 35 degrees Celsius sound travels at a rate of 352meters per sec. if 15degrees Celsius sound travels at 340 meters per sec. How would i write a linear equation that models speed of sound s in terms of air temp T?

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Sra

i need help

exercise 2.5 fifteen question

705 To write a linear equation that models the speed of sound (s) in terms of air temperature (T), we can use the given data points and apply the concept of linear relationships.

We are given two data points: when the air temperature is 35 degrees Celsius, the speed of sound is 352 meters per second, and when the air temperature is 15 degrees Celsius, the speed of sound is 340 meters per second.

Let's define the variables:
- T: Air temperature in degrees Celsius
- s: Speed of sound in meters per second

When defining a linear equation, we usually start with the form y = mx + b, where y represents the dependent variable (in this case, the speed of sound), x represents the independent variable (in this case, the air temperature), m represents the slope, and b represents the y-intercept.

To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)

Using the data points:
(x1, y1) = (15, 340) and (x2, y2) = (35, 352)

m = (352 - 340) / (35 - 15)
m = 12 / 20
m = 0.6

Now that we have the slope, we need to determine the y-intercept (b). We can choose any of the given data points to substitute into the equation.
Let's choose (15, 340):

y = mx + b
340 = 0.6 * 15 + b
340 = 9 + b

Subtracting 9 from both sides:
b = 340 - 9
b = 331

Therefore, the linear equation that models the speed of sound (s) in terms of air temperature (T) is:
s = 0.6T + 331