At the ocean's surface the pressure is 1 atmosphere. At 66 feet below seal level, the pressure is 3 atmosphere. The Relationship between the pressure and the depth is linear.
a. find the independent and dependent variable.
b. create 2 ordered pairs.
c. find the slope.
d. interpret the meaning of the slope.
e. find the prediction equation.
a. The independent variable is the depth and the dependent variable is the pressure.
b. Ordered pairs:
(0, 1) - At the ocean's surface (depth = 0), the pressure is 1 atmosphere.
(-66, 3) - At 66 feet below sea level (depth = -66), the pressure is 3 atmosphere.
c. To find the slope, we'll use the slope equation:
slope = (change in y) / (change in x)
slope = (3 - 1) / (-66 - 0)
slope = 2 / -66
d. The slope represents the rate of change between depth and pressure. In this case, the slope indicates that for every 66 feet of depth, the pressure increases by 2 atmospheres.
e. Using the slope-intercept form (y = mx + b), where y is the pressure, x is the depth, and b is the y-intercept, we can substitute one of the points to find the equation.
Let's use the first ordered pair (0, 1):
1 = (2 / -66)(0) + b
1 = b
Therefore, the prediction equation is:
y = (2 / -66)x + 1
a. The independent variable is the depth, and the dependent variable is the pressure.
b. We can create 2 ordered pairs:
- First ordered pair: (0, 1)
At the ocean's surface, the depth is 0, and the pressure is 1 atmosphere.
- Second ordered pair: (66, 3)
At 66 feet below sea level, the depth is 66, and the pressure is 3 atmosphere.
c. To find the slope, we can use the formula:
Slope = (change in y) / (change in x)
Slope = (3 - 1) / (66 - 0)
Slope = 2 / 66
Slope = 1/33
d. The slope represents the change in pressure for a unit change in depth. In this case, for every 1 foot increase in depth, the pressure increases by 1/33 atmospheres.
e. To find the prediction equation, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept. From the given information, we know that at a depth of 0, the pressure is 1 atmosphere. Thus, the y-intercept (b) is 1.
Therefore, the prediction equation is:
Pressure = (1/33) * Depth + 1
a. In this scenario, the independent variable would be the depth below sea level, and the dependent variable would be the pressure.
b. To create ordered pairs, we can use the given information:
- At the ocean's surface (depth = 0), the pressure is 1 atmosphere. So, the first ordered pair would be (0, 1).
- At 66 feet below sea level (depth = 66), the pressure is 3 atmospheres. Therefore, the second ordered pair would be (66, 3).
c. To find the slope, we can use the formula: slope = (change in y)/(change in x).
- In this case, the change in pressure is 3 - 1 = 2 atmospheres, and the change in depth is 66 - 0 = 66 feet.
- Therefore, the slope = (2 atmospheres) / (66 feet) = 2/66 = 1/33.
d. The slope represents the rate of change of pressure with respect to depth. In this context, the slope of 1/33 means that for every 33 feet of depth increase, the pressure increases by 1 atmosphere. So, the interpretation is that the pressure increases by 1 atmosphere for every 33 feet of depth increase.
e. To find the prediction equation (in slope-intercept form, y = mx + b), we can use any of the ordered pairs.
- We can use (0, 1):
- Using the slope (m) found earlier (1/33), we have: 1 = (1/33)(0) + b.
- Solving for b, we get: b = 1.
- Therefore, the prediction equation is: y = (1/33)x + 1.