You have taken over an abandoned drilling project. After drilling for 2 hours, the depth is 110 feet. After 5 hours, the depth has increased to 114.5 feet.
Write an equation in from y=mx+b to describe the relationship between x, the hours of drilling, and y, the depth of the well
depth , d , = constant * time, t , + constant , b
d = m t + b
110.0 = 2 m + b
114.5 = 5 m + b
------------------------- subtract
- 4.5 = -3 m
so
m = 4.5 / 3
m = 1.5
so
d = 1.5 t + b
110.0 = 1.5*2 + b = 3 + b
b = 107.00
which is the depth at t = 0
d = 1.5 t + 107
(x, y).
(2, 110)
(5, 114.5).
m = (114.5-110)/(5-2) = 1.5.
Y = mx + b.
110 = 1.5*2 + b,
b = 107.
y = 1.5x + 107.
To find the equation that represents the relationship between the hours of drilling (x) and the depth of the well (y), we can use the slope-intercept form of a linear equation, y = mx + b.
First, let's determine the slope (m) of the line. The slope represents the rate of change or how much the depth changes for each hour of drilling. The formula to calculate the slope given two points is:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given information:
- First point: (2 hours, 110 feet) -> (x₁, y₁) = (2, 110)
- Second point: (5 hours, 114.5 feet) -> (x₂, y₂) = (5, 114.5)
Plugging the values into the slope formula:
m = (114.5 - 110) / (5 - 2)
m = 4.5 / 3
m = 1.5
Next, we need to determine the y-intercept (b). The y-intercept is the value of y when x = 0. However, in this case, we do not have that information since we only have data once drilling has already begun. Therefore, we cannot determine the y-intercept using the given information.
Hence, the equation for the relationship between x and y will be represented as y = 1.5x + b, where b is the unknown y-intercept value.