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## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 10

Lesson 1: Heart of algebra- Solving linear equations and linear inequalities — Basic example
- Solving linear equations and linear inequalities — Harder example
- Interpreting linear functions — Basic example
- Interpreting linear functions — Harder example
- Linear equation word problems — Basic example
- Linear equation word problems — Harder example
- Linear inequality word problems — Basic example
- Linear inequality word problems — Harder example
- Graphing linear equations — Basic example
- Graphing linear equations — Harder example
- Linear function word problems — Basic example
- Linear function word problems — Harder example
- Systems of linear inequalities word problems — Basic example
- Systems of linear inequalities word problems — Harder example
- Solving systems of linear equations — Basic example
- Solving systems of linear equations — Harder example
- Systems of linear equations word problems — Basic example
- Systems of linear equations word problems — Harder example

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# Interpreting linear functions — Basic example

Watch Sal work through a basic Interpreting linear functions problem.

## Want to join the conversation?

- how are we supposed to know that t will increase each year?(21 votes)
- Because T=Year. And since years increase annually then T will increase since it represents the year. Hope this helped!(71 votes)

- What do you do with the 100? Why is it there in the equation?(22 votes)
- It is the y-intercept, it is the initial amount paid. You add this to each yearly increasing amount to get your final answer. It is the “b” in the “y=mx+b”(39 votes)

- i'm still a little confused.(18 votes)
- since, 3.53 is multiplied with 't' it means that amount paid by farmers will at least increased by 3.53 million dollars every year.

for example:- in 1991 p=3.53(0)+100 = 100

in 1992 p=3.53(1)+100 = 103.53

in 1993 p=3.53(2)+100 = 107.06(24 votes)

- word problems are hard to solving(19 votes)
- I want David :-<

Sal doesn't think i got this(19 votes) - Hi im pooping right now(18 votes)
- Are there faster ways of solving this?(2 votes)
- Working in your head is usually quicker unless you think really slowly. It gets faster as you practice:)(16 votes)

- World problem are so confusing. I didn't understand anything, how is it possible?!(9 votes)
- why is the sat so hard(8 votes)
- Dang, didn't know farmers had to pay this much over that amount of years! Farming is expensive!(7 votes)

## Video transcript

- The amount of money that
farmers in Massachusetts paid to maintain their
crops between 1991 and 2008 is modeled by the equation above, where P is the amount of
money the farmers paid, in millions of dollars, and t is the year. So, this is how much they
paid in millions of dollars, t is the year, but they're saying assuming 1991 is t equals zero. What does the 3.53 mean in the equation? So, let's look at this. So, in 1991 when t is equal to zero, this whole term is going
to be equal to zero, and the farmers are going to pay, P is going to be a hundred, so they're gonna pay
hundred million dollars in 1991 to maintain their crop. These are all the farmers in Massachusets. Now, as t increments, each
time t increases by one, the amount that the farmers
pay is going to increase by 3.53 times 1. So, one way to think about
it is this is the rate of increase from year to year. As t goes up a year, the
amount the farmers pay is going to increase by
3.53 million dollars. So, let's see which of these choices are consistent with what I just said. (laughs) The cost for maintaining crops was $3.53 million dollars in 1991. No, that's just not true. In 1991, this term is zero, and it was a hundred million dollars. The cost for maintaining crops
was $3.53 million in 2008. No, that's not going to be true either, because it's a hundred million in 1991, and then each year, it's going to increase by 3.53 million. The cost for maintaining crops increased a totally of $3.53 million
between 1991 and 2008. No, it's going to increase
$3.53 million per year, not over the entire time span. The cost for maintaining
crops increased by $3.53 million each year between 1991 and 2008. That is exactly right. Every time t, and we go forward a year, t increases by one. It's going to increase, we're going to have 3.53
times that one higher t, so, we're gonna increase
the whole P by 3.53. That kind of rhymed.