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REVIEW

Remember from way far back, what is slope-intercept form?

Slope- intercept form is: y = mx + b

What is a function?

A function is a relation with only one output per one input.

A relation is a set or ordered pairs.

A function can be written in a few ways, but mostly it is written as f(x) (pronounced f of x.)

A function can have more than one input with the same output, but one input cannot come out with more than one output. (So, in other words, two or more x’s can equal the same y, but one x cannot equal more than one y.)

We can look at the table or the equation to determine if it is a function or not, or we can use the vertical line test on its graph.

We also know that the domain of the function is all the possible x values the function can have.

And also the range is all of the possible y values the function can have.

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POINT SLOPE FORM

So, let’s say in an upcoming test (hint-hint) you are given a word problem that looks something like this:

Johnny just bought some strawberry seeds from his local nursery and is going to plant them. He knows that with each year, if he plants all of his seeds and they all take root, he can get about 2000 strawberries a year. If ten years in he only harvests a total of 19,700 strawberries, how many strawberries will he have in his 16^th year in?

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So, how do we solve a word problem like this?

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FIRST, LET’S TRY IT THE WAY WE KNOW HOW

This is a review of chapter 3, but let’s go over it anyway.

So, we have the slope, which is 2000, so we immediately know where the slope goes in the equation right?

So we know that the equation will look something like:

Y = 2000x

Now, we have the point (10, 19700); so how do we check if this is the right equation? We plug it in!

So:

19700 = 2000(10)

19700 = 20000

But we know 19700 ≠ 20000, so we subtract 20000 from 19700, or 19700 – 20000 = -300. So the equation is

Y = 2000x - 300

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Now that we have the equation, let’s plug in 16 for x and see what we get

So, the equation is:

Y = 2000x – 300

So if we plug in 16 for x (which is the time variable) we get:

Y = 2000(16) – 300

Y = 32000 – 300

Which is to say

Y = 31700 strawberries.

So if Johnny keeps up with 2000 strawberries a year, he’ll grow a total of 31700 strawberries by the 16^th year.

But that was kind of complicated to make and solve, is there maybe an easier way to do it?

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This is where slope-point form comes in

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So what does this tell us?

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SO, WITH VERY LITTLE WORK WE FOUND THE RIGHT ANSWER!

And it happens to be the same answer we got using the way we knew how.

This is the benefit of point-slope form.

Let’s try another example

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NOW THAT WE HAVE OUR POINTS, LET’S PLUG THEM IN!

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ONE LAST EXAMPLE

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BUT WHAT ABOUT 143 AND 167 GALLONS?

We can figure those out just the same. All we need to do is make each of those our new x.

Let’s start with 143 gallons

Our equation is:

Y = 3453 + 60(143 – 59)

Y = 3453 + 60(84)

Y = 3453 + 5040

Y = 8493 miles

Now let’s try 167 gallons

Y = 3453 + 60(167 – 59)

Y = 3453 + 60(108)

Y = 3453 + 6480

Y = 9933 miles

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NOW IT’S YOUR TURN

Solve by using the point-slope form equation, then by plugging in the slope and points to see if it’s right.

Every year Angela grows 2 inches. When she was 5 years old she was 3 feet 6 inches. How tall will she be when she’s 15 years old? How about 20 years old?

Corrin rules over the country of Valla and maintains all of the produce. Their main crop, which keeps the country fed is potatoes. Every year Corrin grows a surplus of 40,000 pounds of potatoes and every year. If the overall surplus of potatoes in 2010 was 160,000 pounds of potatoes, how many pounds of surplus will he have acquired in 2050? 2060? 2070?

Xander is in charge of making sure his kingdom has enough soldiers to defend it, and he’s pretty good at it. Every year he trains 300 new soldiers to maintain his kingdom. If in 1990 Xander had a grand total of 42,000 soldiers, how many soldiers will he have in 2019? How about in 2040?

Recently, a zombie virus has been discovered that turns people into brain-munching zombies. If in the first 3 months the virus infects 3000 people, how many people will the virus infect in 6 months? A year? 20 years? 100 years? (Are we in trouble?)

Dean and Sam kill 40000 monsters a year on average. If their kill count is 120,000 monsters in 2010, how many monsters have they killed in 2019?

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