SOLUTION: After about 8 hours of a steady wind, the height (y) of waves in the ocean is linearly related to the duration of time (x) the wind has been blowing. During a storm with 40-knot wi

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Question 582213: After about 8 hours of a steady wind, the height (y) of waves in the ocean is linearly related to the duration of time (x) the wind has been blowing. During a storm with 40-knot winds, the wave height after 8 hours was found to be 22 feet, and after 23 hours it was 41 feet.
(a) Write a linear equation that relates the height to time.
(b) How long will the wind have been blowing for the waves to be 60 feet heigh?
Answer by ankor@dixie-net.com(22740) (Show Source):
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After about 8 hours of a steady wind, the height (y) of waves in the ocean is linearly related to the duration of time (x) the wind has been blowing.
During a storm with 40-knot winds, the wave height after 8 hours was found to be 22 feet, and after 23 hours it was 41 feet.
:
(a) Write a linear equation that relates the height to time.
find the slope: m =
assign the values as follow
x1=8, y1=22
x2=23, y2=41
:
Find the slope (m)
m = = = is the slope
:
Use the point/slope form to create an equation: y - y1 = m(x - x1)
y - 22 = (x - 8)
y - 22 = x -
y = x - + 22
y = x - +
y = x + ; is the equation
:
(b) How long will the wind have been blowing for the waves to be 60 feet height?
x + = 60
multiply by 15 to get rid of the denominators
19x + 178 = 15(60)
19x = 900 - 178
19x = 722
x =
x = 38 hrs to reach 60 ft waves