To solve this problem we eventually need to write an equation, but first we should come up with two ordered pairs. The ordered pairs represent (week number, number of dumpster loads removed) where week number is the x value or independent variable which is changed and number of dumpster loads removed is the y value or dependent variable that changes when the x value changes. From our given information, we can write our ordered pairs, (5, 50) and (10, 40).
To write the equation, first we need to find the slope, or change in y values divided by the change in x values.
m = change in y/change in x = (50-40)/(5-10) = 10/-5 = -2.
Now that we know the slope is -2, we can use this and one of the points we were given earlier to write an equation in point-slope form.
y = m(x-h)+k
y = -2(x-5)+50
We can simplify this equation by distributing the -2 through the parentheses.
y = -2x + 10 + 50
Finally, we can combine the constant terms by addition.
y = -2x + 60
Therefore, your answer is y = -2x + 60. This means that each week, the number of dumpster loads removed started at 60 and decreases by 2 loads per week.
Hope this helps!
