A chairlift descends from the mountain to pick up skiers at the bottom. After 2 minutes the chairlift is 4,000 ft in the air and after 4 minutes the chairlift is 2,500 ft in the air.
I need help turning this into an equation
the slope of the line is (2500-4000)/(4 - 2) = -750
so, using one of the points,
y-4000 = -750(x-2)
Thank you
What linear form is that equation
To turn this scenario into an equation, we need to establish the relationship between the time (in minutes) and the height (in feet) of the chairlift.
Let's start by assigning variables to the time and height. Let t represent the time (in minutes) and h represent the height (in feet).
Given that after 2 minutes, the chairlift is 4,000 ft in the air, we can create the first data point as (2, 4,000).
Similarly, after 4 minutes, the chairlift is 2,500 ft in the air, giving us the second data point as (4, 2,500).
We can use these two data points to find the equation of a linear relationship between time and height, which can be represented as:
h = mt + b
Now, let's substitute the coordinates from one of the data points into this equation to solve for m and b.
Using the first data point (2, 4,000):
4,000 = 2m + b
Next, substitute the coordinates from the second data point (4, 2,500) into the equation:
2,500 = 4m + b
We now have a system of two equations:
4,000 = 2m + b
2,500 = 4m + b
To solve this system of equations, we can use methods like substitution or elimination. Let's use the elimination method here.
Subtracting the second equation from the first equation, we get:
4,000 - 2,500 = (2m + b) - (4m + b)
1,500 = -2m
Simplifying, we find:
-2m = 1,500
To isolate m, we divide by -2:
m = -1,500 / -2
m = 750
Now that we have the value of m, we can substitute it into any of the original equations to solve for b. Let's use the first equation:
4,000 = 2(750) + b
4,000 = 1,500 + b
By rearranging the equation, we find:
b = 4,000 - 1,500
b = 2,500
Therefore, the equation that represents the relationship between time (t) and height (h) for the chairlift is:
h = 750t + 2,500