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.