Question

The temperature in a city began to decrease at a constant rate once a cold front began to

move in. The temperature was 49°F after 2 hours and 39°F after 6 hours. Suppose x is
the number of hours since the cold front began to move in, and y is the temperature in F.

Answer 1

Explanation:

If we assume that the temperature decreased at a constant rate, we can use a linear equation to model the relationship between the temperature (y) and time (x) since the cold front began to move in.

First, we can find the rate of decrease (slope) of the temperature by using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (2, 49) and (x2, y2) = (6, 39).

slope = (39 - 49) / (6 - 2) = -2.5

So the temperature is decreasing at a rate of 2.5°F per hour.

Next, we can use the point-slope form of a linear equation to write the equation of the line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is one of the points on the line.

Using (x1, y1) = (2, 49) and m = -2.5, we get:

y - 49 = -2.5(x - 2)

Simplifying:

y = -2.5x + 54

So the equation that models the relationship between the temperature (y) and time (x) since the cold front began to move in is y = -2.5x + 54.