Question

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.

f(x) = −4x 60
f(x) = 4x 60
f(x) = −4x 80
f(x) = 4x 80

Answer 1

Keep in mind that \(f(x)=y\)

Answer 2

We have to use `slope intercept form`, I hope you know what that is.

" In week 5, there were 60 dumpster loads of waste removed."
x=5
y=60
(5, 60)

"In week 10, there were 40 dumpster loads removed."
x=10
y=40
(10, 40)

So there are two points which are \((5,\ 60)\ and\ (10, 40) \)

Answer 3

We're using, \(\LARGE m = \frac{(y1 - y2)} {(x1 - x2)}\) then plugging in the numbers from the two ordered pairs we've had before,
So, \(\LARGE m = \frac{(60-40)} {(5-10)}\)

Answer 4

\(\LARGE m = \frac{(60-40)} {(5-10)}\) Simplifies to \(m=−4\)
Thats not the answer tho, now we have to use \(y=mx+b\) to find the \(x\) intercept

Answer 5

So we plug in the numbers to \(y=mx+b\)
\(60 = (-4)(5) + b\)

Simplify:
\(60=−20+b\)
\(60=b−20\)

flip:
\(b−20=60\)

+20, both sides:
\(b−20+20=60+20\)

Answer 6

\(b+−20+20=60+20\)
Parenthises/combine like terms:
\((b)+(−20+20)=(60+20)\)
Combine like terms:
\(b=?\)

Answer 7

After you find what b=
Plug all the numbers into \(y=mx+b\)
Then you have your answer,
\(\color{#99ff}{\text{Originally Posted by}}\) @supie
Keep in mind that \(f(x)=y\)
\(\color{#99ff}{\text{End of Quote}}\)

Answer 8

\(\color{#0cbb34}{\text{Originally Posted by}}\) @supie
We're using, \(\LARGE m = \frac{(y1 - y2)} {(x1 - x2)}\) then plugging in the numbers from the two ordered pairs we've had before,
So, \(\LARGE m = \frac{(60-40)} {(5-10)}\)
\(\color{#0cbb34}{\text{End of Quote}}\)
slope formula = y2-y1/x2-x1

Answer 9

so in this way u are incorrect

Answer 10

Good catch
" In week 5, there were 60 dumpster loads of waste removed." \(>\) \((5,\ 60)\)
"In week 10, there were 40 dumpster loads removed." \((10,\ 40)\)
Slope formula is \(m=\frac{y_2-y_1}{x_2-x_1}\)
Our two ordered pairs are \((5,\ 60)\ \&\ (10,\ 40)\)
y2=the second 'y' value of the two ordered pairs
y2=the first 'y' value of the two ordered pairs

x2=the second x value of the two ordered pairs
x1=the first x value of the two ordered
Remember that an ordered pair is \((x,\ y)\)
The means that
y2=40
y1=60

x2=10
x1=5
So we plug in the values into the formula:
\(\LARGE\frac{y_2-y_1}{x_2-x_1}\longrightarrow \frac{40-60}{10-5}\)
So then to simplify \(\frac{40-60}{10-5}\) to get what \(m\)(the slope) equals.
The way we do that is subtract straight across, 40-60 & 10-5
\(\LARGE\frac{40-60=-}
{10-5=}\frac{-20}{5}\)
Which equals -4

So I think we got the same answer for some reason:
\(\color{#0cbb34}{\text{Originally Posted by}}\) @supie
\(\LARGE m = \frac{(60-40)} {(5-10)}\) Simplifies to \(m=−4\)
Thats not the answer tho, now we have to use \(y=mx+b\) to find the \(x\) intercept
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 11

y=0x+40=60/10-5