As a diver descends into fresh water we have determined that for every 10 meters of depth the pressure on the diver increases by one atmosphere. Find the equation of the line representing this relationship if we know that when the diver is at a depth of 25 meters there is a pressure of 3.5 atmospheres
let's take some ordered pairs that fit the above description.
(25,3.5) , (35, 4.5), (45, 5.5), (15, 2.5 , (5, 1.5)
etc
in each case of pairs, the slope is 1/10 , and the function is linear.
so A = (1/10)m + b
using the given point (25,3.5)
3.5 = (1/10)(25) + b
b = 1
A = (1/10)m + 1
To find the equation of the line representing the relationship between depth and pressure, we can use the slope-intercept form of a linear equation: y = mx + b.
In this case, the depth represents the independent variable x, and the pressure represents the dependent variable y. We are given that for every 10 meters of depth, the pressure increases by one atmosphere. So, the slope (m) of the line can be calculated by dividing the change in pressure (Δy) by the change in depth (Δx):
m = Δy / Δx = 1 atmosphere / 10 meters = 0.1 atmospheres per meter.
Now that we have the slope, we need to find the y-intercept (b). We are given that when the diver is at a depth of 25 meters, the pressure is 3.5 atmospheres. We can substitute these values into the equation to solve for b:
y = mx + b
3.5 = 0.1 * 25 + b
3.5 = 2.5 + b
b = 3.5 - 2.5
b = 1
Therefore, the equation of the line representing this relationship is:
pressure = 0.1 * depth + 1
This equation shows that the pressure (in atmospheres) is equal to 0.1 times the depth (in meters) plus 1.