The table shows the height of an elevator above ground level after a certain amount of time. Let y stand for the height of the elevator in feet and let x stand for the time in seconds. Which equation models the data below?
Time (s) Height (ft)
10 235
20 220
40 190
60 160
let's assume the relationship is linear
slope between first pair of points = (220-235)/(20-10) = -15/10 = -1.5
so y = -1.5t + b
using (10,235)
235 = -1.5(10) + b
235 = -15 + b
b = 250
y = -1.5t + 250
testing for last data value
when t=60
y = -1.5(60) + 250 = 160 , yeah!
Well, this table definitely gives new meaning to the phrase "going down!"
But let's focus on finding an equation to model this clearly descending elevator. Since the height is decreasing as time increases, we can reasonably expect a linear equation. And what's the standard form for a linear equation? That's right, it's y = mx + b.
Now, let's think about the slope of the line. From the data, we can see that for every 20 second increase in time, the height decreases by 15 feet. So, the slope is -15/20, which simplifies to -3/4.
Now, we need to find the y-intercept, which is the height when x (time) is 0. From the table, we can see that when x is 0, the height is 235. Therefore, the y-intercept is 235.
Now we can put all this together and create our equation: y = (-3/4)x + 235.
So, the equation that models this data is y = (-3/4)x + 235. It's all downhill from here!
To find the equation that models the given data, we need to determine the relationship between the time (x) and the height (y) of the elevator.
We can start by examining how the height changes over time. Looking at the table, we can see that as time increases, the height decreases.
One way to represent this relationship is with a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can choose any two points from the table and calculate the change in y divided by the change in x.
Let's take the points (10, 235) and (60, 160):
Slope = (160 - 235) / (60 - 10)
= -75 / 50
= -1.5
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - y₁ = m(x - x₁)
Choosing point (10, 235) as our reference point:
y - 235 = -1.5(x - 10)
Expanding and rearranging the equation:
y - 235 = -1.5x + 15
y = -1.5x + 250
Therefore, the equation that models the given data is y = -1.5x + 250.
To find the equation that models the given data, we need to determine the relationship between the time (x) and the height (y) of the elevator. One common type of relationship is a linear equation, which can be represented in the form y = mx + b, where m is the slope and b is the y-intercept.
To determine the slope (m) of the linear equation, we can calculate the change in height over the change in time. Let's look at the first two data points: (10, 235) and (20, 220).
Change in height = 220 - 235 = -15
Change in time = 20 - 10 = 10
Slope (m) = Change in height / Change in time = -15 / 10 = -1.5
Now, let's substitute one data point (10, 235) into the linear equation to solve for the y-intercept (b):
235 = -1.5 * 10 + b
235 = -15 + b
b = 235 + 15 = 250
Therefore, the equation that models the given data is:
y = -1.5x + 250