Project Math Access DVD 03 - Algebra - Part 12
Transcript Start
Audio Description: Part twelve; solving equations using the braillewriter and graphing.
TEACHER: Number 12 says...
BRANDON: ...12. Graph 2x + 3y = 6.
TEACHER: What are we gonna do with this one?
BRANDON: So this one's in standard form...
TEACHER: Right. Which is commonly known as Ax + By = C.
TEACHER: Okay. So how do we graph that?
BRANDON: Hoooo boy. These are ones I have trouble with.
TEACHER: Okay, how can I help? There are a couple of solutions. You can either turn it into Y intercept form, that's a big hassle, or you can... pick a value for X and plug in the Y value. Right? So let's pick something real simple. How about if you pick zero for X?
BRANDON: Yeah, 2 times zero is zero, Plus....
TEACHER: You might need the brailler to write this down.
BRANDON: Yeah, so zero plus 3 times 2 equals 6.
TEACHER: Okay.
BRANDON: So 2 is our Y value.
Audio Description: The teacher writes the equation as Brandon speaks it.
BRANDON: So 3 times 2...
TEACHER: What's 3 times 2?
BRANDON: 3 times 2 is 6.
TEACHER: Okay.
BRANDON: So 3y equals 6.
TEACHER: So 6 equals 6? Right?
BRANDON: Right.
TEACHER: So that's good. That's what you want. You want to plot the point there.
BRANDON: Right.
TEACHER: So what would the coordinates of that point be? You plugged in what for X?
BRANDON: Plugged in zero.
TEACHER: Good. You used what for Y?
BRANDON: 2
TEACHER: Good.
TEACHER: So your coordinates are that point....
BRANDON: Zero, 2
TEACHER: Zero, 2.
BRANDON: So zero on the X...
TEACHER: Don't go anywhere, you're still at the origin. and then what?
BRANDON: ...then 2... on the Y
BRANDON: Up 2
TEACHER: Right.
TEACHER: Alright, how many points do we need to make a line? ... minimally?
BRANDON: Two.
TEACHER: Two, so we have to do this again. So, pick a value for X, and find the value for Y.
BRANDON: Let's see... 3x...
TEACHER: Wait a minute, where do you get 3x?
TEACHER: It's 2x plus...
BRANDON: Yeah. 2x equals 3y.
TEACHER: What are you going to choose for X?
BRANDON: Times 1
TEACHER: Good, 1 for X.
BRANDON: So 2...
TEACHER: It might help to write it down.
BRANDON: Yeah, 2... [sound of braillewriter] 2 plus 3 Y... equals 6... hmmm. I might need to solve this equation.
TEACHER: Right, because you need to find out what Y equals.
BRANDON: ... so 3y equals 4...
TEACHER: Okay.
BRANDON: ...Y equals... four-thirds.
TEACHER: Okay.
BRANDON: Fourthirds.
TEACHER: So that might be tricky to plot.
TEACHER: If you were to turn that into a mixed number, what would it be?
BRANDON: Hmmm... One and one third.
TEACHER: Okay.
TEACHER: So you plot that at one and one third for the Y.
BRANDON: Right.
TEACHER: And then the one....
BRANDON: ...one and one third.
BRANDON: From the
Audio Description: Brandon has his hand on the origin.
BRANDON: So 1...
TEACHER: Careful
TEACHER: your X coordinate is 1. Your X coordinate is 1.
Start at the origin. X is 1.
BRANDON: X is 1... Oh, then the Y is the 1 over 3?
TEACHER: One and one third.
BRANDON: So we go up 1...
TEACHER: And then a little bit more. It's really hard on this graph paper to make an exact measurement. What you might to do is to plug in a different value until you get 2 whole numbers... to make it easier. So let's pick a different value... just to be on the safe side.
BRANDON: For Y?
TEACHER: If you pick for Y then you're solving for X. Either way you can do it.
TEACHER: Pick a number out of the air.
BRANDON: 2.
TEACHER: Okay, great. 2 for X. That would be 2 times 2, right? Because it's 2X plus 3y. So that is what? Write it down.
BRANDON: 2 plus 3y...
TEACHER: No.
BRANDON: Why?
TEACHER: Because it was 2x,
TEACHER: and you chose 2 for X...
BRANDON: 4, plus 3y.
TEACHER: Good.
BRANDON: 4 plus 2y
TEACHER: Equals...
BRANDON: Oops...
TEACHER: That's fine.
BRANDON: Equals 6, now I subtract 4.
3y... equals 2. So Y equals one and one-half.
TEACHER: Are you sure? I don't think so.
BRANDON: two-thirds...
TEACHER: Y equals two-thirds
TEACHER: So again, that one's a little trickier to graph. So let's try an odd number since one you picked was zero...
BRANDON: One.
TEACHER: We already did 1. Let's try 3.
BRANDON: Four...
TEACHER: No, 2x+3y.
TEACHER: Start with your original equation, write that down; 2x + 3y. Plug in 3 for the X...
BRANDON: So 6 plus 3y equals 6. So I subtract 6, so 3y equals zero so Y equals zero.
TEACHER: Good.
TEACHER: So your coordinates then would be...
BRANDON: Would be 3, zero.
TEACHER: Three and zero. So plot those.
BRANDON: Three, zero. So... We need... x,y... Three, zero... AIways starting from the origin, go to the right 3.
Audio Description: Brandon places a point.
TEACHER: Alright, put it down, good.
We're going to lay down my pencil across those points from the start to make it easier.
Audio Description: Brandon grabs a Wikki Stix.
TEACHER: Now all you have to do is line up the Wikki Stix on top of the pencil.
BRANDON: On top...
TEACHER: With out wiggling. I mean,...above, or beIow...actuaIIyI have my pencil lined up above the point, so put the Wikki Stix underneath... or below, rather. Push it down.
Audio Description: One end of the Wikki Stix is curved.
TEACHER: I think a ruler would be better.
BRANDON: (laughs) Yes, so much better.
TEACHER: Pretty good. The end of this line is really, really crooked.
Audio Description: The teacher straightens the Wikki Stix.
TEACHER: Alright. Good job. That was a tough problem. You stuck with it.