Scientific Model

Question

A scientific model is used to predict the average global high temperature on earth by anaylizing the data from previous years. In 1910, the temperature was 66∘ F However, the temperature has grown to 73.7∘ F in 1980.

 Find an equation in the form T=ax+b, where x is the number of years since 1910 and T is the average gobal high temperture on Earth.

Answer 1

You are finding a linear equation, in the form y = mx + b (or in the problem T = ax + b.)

The problem gives you two points on the line in the problem, "In 1910, the temperature was 66∘ F" is (0, 66) and "However, the temperature has grown to 73.7∘ F in 1980" is (70, 73.7). I can use these two points to determine the slope of the line which is a, a = (y1 - y2)/(x1 - x2). It does not matter which point I pick to be (x1, y1) and which to be (x2, y2) in this formula. a = (66 - 73.7)/(0 - 70) = -7.7 / -70 = 1.1 / 10 = .11 or a = (73.7 - 66) / (70 - 0) = 7.7 / 70 = 1.1 / 10 = .11. We have the y-intercept point, since at x=0 we know T = 66, so b = 66 ( 66 = .11(0) + b = 0 + b = b).

The equation is T = ax + b = .11x + 66, where x is the number of years since 1910 and T is the average global high temperature on Earth in degrees Fahrenheit.

.