A meteorologist finds that the temperature at the
6000-foot level of a mountain is 76°F and the temperature at the 12,000 foot level
of the mountain is 49°F. Write a linear equation to represent the temperature T at ar
elevation of x, where x is in thousands of feet.
we have te ordered pairs
(6,000,76) and (12,000,49)
step 1
find the slope
m=(49-76)/(12,000-6,000)
m=-27/6,000
simplify
m=-9/2,000
step 2
Find the equation in slope intercept form
T=mx+b
we have
m=-9/2,000
point (6,000, 76)
substitute
76=(-9/2,000)*6,000+b
solve for b
76=-27+b
b=76+27
b=103
therefore
teh linear equation is
T=-(9/2,000)x+103