Question

It is 76º F at the 6000-foot level of a mountain, and 49º F at the 12,000-foot level of the mountain. Write a linear equation, in slope-intercept form, to find the temperature T at an elevation e on the mountain, where e is in thousands of feet.

Answer 1

Answer:

Step-by-step explanation:

It is 76 degrees F at the 6000-foot level of a mountain, and 49 degrees

F at the 12000-foot level of a mountain.

Write a linear equation to find the temperature T at an elevation e on the

mountain, where e is in thousands of feet.:

:

Find the slope using the slope formula: m = %28y2-y1%29%2F%28x2-x1%29

Assign the given values as follows

x1 = 6 (for 6000 ft); y1 = 76

x2 = 12(for 12000ft); y2 = 49

:

m = %2849-76%29%2F%2812-6%29 = %28-27%29%2F6 = -9%2F2

;

 

Use the point slope equation y - y1 = m(x - x1) so create the equation

y - 76 = -9%2F2(x - 6)

y - 76 = -9%2F2x - (-27)

y - 76 = -9%2F2x + 27 + 76

y = -9%2F2x + 103; is the equation

Using e and T

T = -9%2F2e + 103

:

where elevation is the horizontal and Temp is the vertical

;