The air temperature decreases by about 1 degree Fahrenheit for each 300 feet of altitude.

a) Find a function T(x) for the temperature at an altitude of x feet if the sea-level temperature is 45∘F.

(b) Find T(1000). [Round to two decimals]

I considered two sets of points: (0,45) and (300,1). then I calculated the slope: m=-0.15 and from there used the formula y=mx+b, which resulted in y=-0.15x + 45. I wondered if this is correct?

T(x) = 45 - x/300

(300,1) is not a point on the line. x has to increase by 300 for T to drop by 1°. Thus, (300,44) is the point you are after.

Thank you!:)

Yes, your approach is correct. To find the function T(x) for the temperature at an altitude of x feet, you can consider the two points (0, 45) and (300, 44) since the temperature decreases by about 1 degree Fahrenheit for each 300 feet of altitude.

Using the slope-intercept form of a linear equation (y = mx + b), where m is the slope and b is the y-intercept, you can calculate the slope:

m = (change in y) / (change in x) = (44 - 45) / (300 - 0) = -1 / 300

Next, you can substitute the slope and one of the given points (0, 45) into the equation y = mx + b and solve for b:

45 = (-1/300)(0) + b
45 = b

Now that you have the equation in the form y = mx + b, you can replace y with T(x) and x with x to get the function T(x):

T(x) = -1/300 * x + 45

To find T(1000), you can substitute x = 1000 into the function:

T(1000) = -1/300 * 1000 + 45
T(1000) = -10/3 + 45
T(1000) ≈ 44.67

Therefore, T(1000) is approximately 44.67 degrees Fahrenheit when the sea-level temperature is 45 degrees Fahrenheit.

Yes, your approach is correct. To find the function T(x) for the temperature at an altitude of x feet, you can use the slope-intercept form of a linear equation, which is y = mx + b. In this case, y represents the temperature, x represents the altitude, m represents the slope, and b represents the y-intercept.

In your case, you correctly identified two points on the line: (0, 45) and (300, 1). The first point represents sea-level temperature, so we can use it as the y-intercept. The second point represents the change in temperature at an altitude of 300 feet.

To find the slope (m), you can use the formula:

m = (change in temperature) / (change in altitude)

In this case, the change in temperature is 1 degree Fahrenheit and the change in altitude is 300 feet. So the slope (m) is:

m = 1 / 300 = 0.00333... (rounded to five decimal places)

Now, you can plug in the values of m and b into the equation y = mx + b:

T(x) = 0.00333x + 45

This is the function T(x) that represents the temperature at an altitude of x feet, given that the sea-level temperature is 45°F.

To find T(1000), you can simply substitute x = 1000 into the function:

T(1000) = 0.00333(1000) + 45

Calculating this, you get:

T(1000) = 3.33 + 45 = 48.33°F

So, T(1000) is approximately 48.33°F (rounded to two decimal places).