TOXIC CLEANUP
Three months after cleanup began at the dump site, 800 cubic yards of toxic waste had yet to be removed. Two months later, that number had been lowered to 720 cubic yards.
a. Write an equation that mathematically describes the linear relationship between the length of time x (months) the cleanup crew has been working and the number of cubic yards y of toxic waste remaining.
b. Use your answer to part a to predict the number of cubic yards of waste still be on site 1 year after the cleanup project began.
Treat the question as if you had two ordered pairs
(3,800) and (5,720)
slope = (720-800)/(5-3) = - 40
using(3,800)
y - 800 = -40(x-3)
y = -40x + 920
b) so after 1 year, x = 12
y = -40(12) + 920 = 440
state your conclusion using the proper units
a. To write the equation that describes the linear relationship, we can use the slope-intercept form of a linear equation:
y = mx + b
In this case, the number of cubic yards remaining (y) is dependent on the length of time the cleanup crew has been working (x). Let's assign "x" as the number of months and "y" as the number of cubic yards remaining.
We are given two points on the line:
(3, 800) - three months after cleanup began
(5, 720) - two months later
To find the equation, we need to find the slope (m) and the y-intercept (b).
First, let's find the slope:
m = (y₂ - y₁) / (x₂ - x₁)
m = (720 - 800) / (5 - 3)
m = -80 / 2
m = -40
Now, let's use one of the given points (3, 800) to find the y-intercept (b) using the slope-intercept form:
800 = -40(3) + b
800 = -120 + b
b = 800 + 120
b = 920
So the equation that mathematically describes the linear relationship is:
y = -40x + 920
b. To predict the number of cubic yards of waste still on-site one year after the cleanup project began (x = 12), we can substitute x = 12 into the equation and solve for y:
y = -40(12) + 920
y = -480 + 920
y = 440
Therefore, 440 cubic yards of waste are predicted to still be on-site one year after the cleanup project began.