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.
find the slope: m = {{{(y2-y1)/(x2-x1)}}}
assign the values as follow
x1=8,  y1=22
x2=23, y2=41
:
Find the slope (m)
m = {{{(y2-y1)/(x2-x1)}}} = {{{(41-22)/(23-8)}}} = {{{19/15}}} is the slope
:
Use the point/slope form to create an equation: y - y1 = m(x - x1)
y - 22 = {{{19/15}}}(x - 8)
y - 22 = {{{19/15}}}x - {{{152/15}}}
y = {{{19/15}}}x - {{{152/15}}} + 22
y = {{{19/15}}}x - {{{152/15}}} + {{{330/15}}}
y = {{{19/15}}}x + {{{178/15}}}; is the equation
:
(b) How long will the wind have been blowing for the waves to be 60 feet height?
{{{19/15}}}x + {{{178/15}}} = 60
multiply by 15 to get rid of the denominators
19x + 178 = 15(60)
19x = 900 - 178
19x = 722
x = {{{722/19}}}
x = 38 hrs to reach 60 ft waves