linear modeling

Question

after about 9 hours of a steady 50 knot wind,the height of waves in the ocean was found to be 23 feet, and after 24 hours it was 40 feet. write the equation.

Answer 1

Start with two point form:

(y - 23) / (x - 9) = (40 - 23) / (24 - 9)

(y - 23) / (x - 9) = 17 / 15

15(y - 23) = 17(x - 9)

15y - 345 = 17x - 153

Answer 2

Here we can make a linear equation of the form y=mx+b to describe the change in the ocean's height. y will be the height in feet and x will be time in hours. We have basically been given two coordinate pairs, (9 hours, 23 feet) and (24 hours, 40ft)

Try using the formula

(y₁-y₂)/(x₁-x₂) = m to find the slope and then you can use known information to solve the y=mx+b for b by plugging in one of the x, y pairs

(23-40)/(9-24)=17/15

y=(17/15)x+b

plug in x=9 y=23

23=(17/15)*(9)+b and solve for b (: