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Robert McKeown: Our next problem asks us to find

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the x intercept and the y intercept of a line.

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Graphically, it's going to look something like

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this. There's our line. I've drawn it with a

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negative slope. And we want to find our x axis

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intercept. And we want to find our Y axis

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intercept.

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Now remember that the north south axis is our Y

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axis, and the East West is our x axis. So if I

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have seven x plus three, y is equal to negative

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12, I can find the equation of the line by

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solving for y. So solve for y to find the

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equation for that this line. And so I could

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rewrite this as three y is equal to negative 12

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minus seven x, I'm essentially subtracting seven

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x on both sides of the expression. And then y is

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going to be equal to 12 plus seven x over three,

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and that whole thing is going to have a negative

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sign in front of it. Now, I didn't actually need

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to do that, to answer the question. So if I want

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to find the x axis intercept, well, what is y at

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the x axis intercept, while y is always equal to

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zero, y is equal to zero x is going to be equal

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to some number, except at the origin where it's

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equal to zero. So to find the x axis intercept,

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set y equal to zero and solve for x.

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So I've got three. Well, maybe I'll start with

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this equation up here, I'll go back to the

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original equation. So I'm going to have seven x

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plus three times zero. And that's equal to

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negative 12. And so I'm going to have x is equal

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to negative 12 over seven

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and to find the y axis intercept, set x equal to

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zero and solve for y. And we did this in an

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earlier problem. And so I'll start with the

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original expression, because that's easy to work

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with God seven times zero plus three y is equal

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to negative 12. Three y is equal to negative 12.

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And y the y intercept is equal to negative four.

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So this is my x axis intercept and this is my Y

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axis intercept. Here we are an ALEKS. the y

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intercept is negative four. And the x axis

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intercept is negative 12 over seven, and let me

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just double check that and let's see if we have

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the right answer. And we do so we successfully

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found the y intercept and the x intercept for

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that equation. So we've got this royal Fruit

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Company and they create two different types of

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fruit drinks. wine has 60% pure fruit juice, the

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other 85% pure fruit juice and I'd like to make

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a third drink that contains 75% fruit juice. So

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how many pints a pint is close to half a liter.

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And it's a it's a very British measure of union.

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And you can see that British influence in

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Toronto, Toronto, when you go out to a bar and

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you order a beer, you often order a pint of

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beer. So we want to find how many pints of each

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pure fruit juice to combine in order to get 80

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pints of a combined mixture. So here are some

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equations that are going to help us the first

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equation is that we've got in type one, we have

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60%, pure fruit juice. And if we multiply that

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by the weight, how much as a percentage, the

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proportion of type one to use. And add that with

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the type two mixture, which is 85% pure. We want

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to combine those two so that we have that third

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drink that contains 75% pure fruit juice. A

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couple other equations we need. If we want to

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know how many pints of type one we'll need,

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well, we want a total of 80. And we multiply

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that by the proportion. The weighting of type

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one, we will get how many pints of the first

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fruit juice we need. Similarly, if we want to

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know how many pints of the second type we need,

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well, we can take 80 and multiply that by the

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way of this, the second type of fruit juice.

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So it looks like we've got two, two unknowns

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here. But what we can do is we can make our life

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a little bit easier because we know that and we

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use this very often in economics and finance,

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that the proportion of the first type of juice,

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plus the proportion of the second type of juice

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has to be equal to one. We can't use a negative

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proportion. So how much of the first use type we

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use has to be greater than or equal to zero. And

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similarly, the waiting on the second type also

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has to be greater than or equal to zero. And it

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can't be greater than one, it can't be greater

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than 100% can't use more than 100% of one juice

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type. We can't do that. That would be physically

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impossible. So now we've got a whole bunch of

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expressions that can help us solve a word

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problem like this. I like to start with equation

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three. And we can see here that if I rearrange

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this, the weighting of the second juice type is

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equal to one minus the weighting on the first.

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And so I can take this expression and plug it

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into the first equation. So the first equation

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becomes 60% pure juice times wait one plus 85%

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pure juice times one minus w one is equal to

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75%. We want to get that 75% pure juice.

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multiplying this out we get 60% times w one plus

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85% minus 85%. w one is equal to 75%. Now I can

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collect like terms

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And we get minus 25% w one is equal to minus

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10%. And therefore w one is going to be equal to

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10 over 25, which is equal to two fifths to over

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five.

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What's w two? Well, W two is equal to one minus

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w one, which is equal to one minus two over

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five, which is equal to five, minus two over

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five, which is equal to three over five. Right?

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You see how much faster I'm going if you watch

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the first topic videos, I go over that really

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slowly. Now I'm going much faster. And you

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should be able to go this fast too. As you

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practice in practice and practice, you're going

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to get better and better and better at it. Now

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that I know what my weights are, I can answer

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the question right? The question is asking us

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how many pints so wants to know the number of

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pints, the amount of pints of type one for a

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drink, and the number of pints in type two. So

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the pints of one is going to be equal to 80

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total clients, multiplied by two over five. And

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that's equal to 160 over five, but if I don't

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want to use a calculator, I can see that this is

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also equal to 40 over five times four, which is

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equal to eight times four, which is equal to 32.

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So that's a fairly straightforward way of

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calculating that now we go with pints to how

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many pints of the second type of fruit juice Are

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we going to need? Well, I mean, there's other

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ways to do this, but I'll do it belong way.

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And like I did before, I'm going to have 240

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over five. It's like 40 over five, which is

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going to be equal to eight times six, and I get

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eight times six, which is going to be equal to

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48.

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Here we are on ALEKS. Let's see if we've got the

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right answer. So for the first fruit drink, we

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had 32 pints. And for the second fruit drink, we

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had 48. Notice that the sum of those two is 80.

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So that's a good sign. We have the right answer.

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I'll click the checkbox and we got the right

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answer.