A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 60 dumpster loads of waste removed. In week 10, there were 40 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week.
A. f(x) = −4x + 60
B. f(x) = 4x + 60
C. f(x) = −4x + 80
D. f(x) = 4x + 80
help me plz
The answer is A, f(x)= -4x + 60
you have two data points ... (5,60) and (10,40)
see which equation they fit
To find the equation in function form that represents the amount of trash removed each week, we can use the information given in week 5 and week 10.
Let's assign the amount of trash removed each week as "y" and the number of weeks as "x".
In week 5, there were 60 dumpster loads of waste removed, so we have the point (5, 60).
In week 10, there were 40 dumpster loads removed, so we have the point (10, 40).
To find the equation, we need to determine the slope (m) and the y-intercept (b) using these two points.
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values, we get:
m = (40 - 60) / (10 - 5) = -20 / 5 = -4
Now that we have the slope (m), we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Choosing one of the given points (5, 60), we substitute the values:
y - 60 = -4(x - 5)
Now, let's simplify it:
y - 60 = -4x + 20
To represent the amount of trash removed each week in function form (f(x)), we rearrange the equation:
y = -4x + 20 + 60
y = -4x + 80
Comparing this equation to the options given, we can see that the correct answer is C. f(x) = -4x + 80.
To determine the equation in function form that represents the amount of trash removed each week, we need to understand the relationship between the week number and the number of dumpster loads removed.
Given that the reduction in the amount of waste each week is linear, we can consider the equation of a straight line in slope-intercept form: y = mx + b, where y represents the number of dumpster loads, x represents the week number, m represents the slope, and b represents the y-intercept.
In this case, the slope will represent the rate at which the amount of waste is reducing each week, and the y-intercept will represent the initial amount of waste in week 0.
Using the given information, we have the following data points:
Week 5: Number of dumpster loads = 60 (x = 5, y = 60)
Week 10: Number of dumpster loads = 40 (x = 10, y = 40)
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
m = (40 - 60) / (10 - 5)
m = -20 / 5
m = -4
Now we can substitute the slope (m) and one of the data points (x, y) into the slope-intercept form equation y = mx + b to find the y-intercept (b):
60 = -4(5) + b
60 = -20 + b
b = 80
Now that we have the slope (m = -4) and the y-intercept (b = 80), we can write the equation in function form:
f(x) = -4x + 80
Therefore, the correct answer is option C: f(x) = -4x + 80.