Project Math Access DVD 03 - Algebra - Part 09
Transcript Start
Audio Description: Part nine; solving equations using graphing; example three.
BRANDON: Graph y=2x-1.
Ahhh. Nicely set up already in slope intercept form.
TEACHER: Absolutely.
BRANDON: These are the equations we like. Oh, yes. We love these equations.
TEACHER: Make it happen.
BRANDON: We want to marry these equations. Ha ha ha. Get it?
TEACHER: Wow. No, I'm not quite that close to my equations, sorry.
BRANDON: (laughs)
TEACHER: Alright, so how do we graph this equation?
BRANDON: So, this is already set up in this nice... nicely set up slope intercept form.
TEACHER: We've stated that. Y=2x-1.
BRANDON: 2x-1. So first we need the Y intercept, which is negative 1. So, that means we go to to the left 1.
TEACHER: Careful. That's your Y intercept. So what are you doing with it?
BRANDON: Y... X... Y... wait... Yes, so we want to go down 1.
TEACHER: Very good.
BRANDON: Down 1, always start from the origin...
TEACHER: Because the Y intercept, if you were to write the coordinates of that point, the X coordinate would be zero.
BRANDON: Zero.
TEACHER: And the Y coordinate would be... so for here it's negative 1.
BRANDON: Right. So, from the origin we want to go down 1
TEACHER: Good.
BRANDON: Plot the point.
Audio Description: Brandon grabs one of the points cut from the Wikki Stix.
BRANDON: Always make sure you're plotting the points.
TEACHER: Plotting points is good.
And what other information do you need from there?
BRANDON: We need the slope...
TEACHER: Okay.
BRANDON: Which is 2...
TEACHER: How do you know the slope is 2?
BRANDON: Because that's the form for equation of the line.
TEACHER: Alright, so 2 is your slope. The standard, no not the standard, the slope intercept form. for this is Y=mX+B, and m being the slope.
BRANDON: Now, remember slope are fractions so that's 2 over 1.
TEACHER: Right, and how do you know which way to go?
BRANDON: Uhmm, if it's... it's rise over run, slope is always rise over run. And if it's negative, you go down otherwvise, if it's positive you go up for the rise.
TEACHER: Right, so you're at negative 1, so are we rising or are we running?
BRANDON: We are rising.
TEACHER: Okay, good.
BRANDON: We go up 2, and over 1
TEACHER: Good.
BRANDON: Plot the point
TEACHER: Plot your point.
TEACHER: What are the coordinates of that point?
Trick question.
BRANDON: Oooo...
TEACHER: This is where I can see if you can interpret the graph.
BRANDON: Oh boy.
TEACHER: You're plotting the point, you could also do the math calculations and figure it out. I want you to be able to tell me what the coordinates of that point are.
BRANDON: 1,1.
TEACHER: Good.
BRANDON: 1,1.
TEACHER: Alright. 1,1. Now what? When we're graphing this line, how many points...
BRANDON: ...at least 3 points.
TEACHER: Three points would make it easier.
BRANDON: Two points are good, but 3...
TEACHER: But 3 are a little straighter. The more points you have, the straighter the line. In terms of Wikki Stix Land.
BRANDON: (chuckles) Welcome to Wikki Stix Land.
TEACHER: (laughs)
TEACHER: So, from that 1, 1 point, what do you do?
BRANDON: We go up 2, and over 1.
TEACHER: Why?
BRANDON: Because that's the slope.
TEACHER: Because you have to use the slope which is rise over run. Good.
BRANDON: Yes, and we plot the point.
TEACHER: And what are the coordinates of that point?
BRANDON: Oh boy, the questions I'm not expecting.
TEACHER: That's alright. Expect the unexpected, Brandon.
BRANDON: Let's see... so X comma Y, so We're at 1, 2,... 2, 3.
TEACHER: Let me see... yep.
BRANDON: Okay, so we have 3 points. So we take our Wikki Stix.
TEACHER: Uh, hmmm. And what do we do with that Wikki Stix?
BRANDON: And we place it over all 3 points.
TEACHER: What do you do with it first?
BRANDON: Oh, can't forget to make it taut.
TEACHER: But you have to keep it taut when you're laying it down. because if you pull it taut and then you wiggle it and squish it up you're going to get this goofy looking line that won't serve your purpose. It won't do you any good. Let's say you need other information on that graph, Right? Let's say you're plotting prices of items at the grocery store.
BRANDON: Okay.
TEACHER: And you have, you know, your apples for so much a pound and the pears, and you want to figure out what are oranges going to be if they're all in a gradual... increase.
BRANDON: Right.
TEACHER: and you could check that out from this graph. Now make sure that across all your points.
Audio Description: The line does not intersect 0, -1.
TEACHER: Let's see if you can find your points.
TEACHER: Ha, ha, haaaa. Alright, do you think that line is straight?
BRANDON: Definitely!
TEACHER: No, I don't think so...
BRANDON: Especially on this end.
TEACHER: What do you think might be really helpful in this case? That you don't like to use?
BRANDON: Argh, the ruler.
TEACHER: The ruler.
TEACHER: I don't have that today, I'm going to straighten it out for you.
Audio Description: The teacher pulls the Wikki Stix taut.
BRANDON: Whew.
TEACHER: Miss Seleb to the rescue, I know.
These are kind of hard to lay across there. That's pretty good. Alright. Close enough. So there's your equation 1.
BRANDON: Yes.
TEACHER: ...graphed.
TEACHER: Good job. Now what?
Can you tell me another point on that line?
I know, surprise question.
BRANDON: Oh man.
Audio Description: Brandon's fingers remain steady over the points.
TEACHER: How would you find another point on that line?
BRANDON: Well, I'll keep going from the slope.
TEACHER: Well, that would be the cheater way to do it.
BRANDON: The cheater way?
TEACHER: Yep.
TEACHER: You have your line here, how can you find another point on the line?
BRANDON: Oh, here... wait a minute.
TEACHER: Find where that line...
BRANDON: Where the line crosses, 2 others
TEACHER: Two other lines.
BRANDON: Right.
TEACHER: On the raised line. So where are the coordinates of that point? You can do this. Put your head up. That's better.
Audio Description: Brandon counts up the Y axis.
TEACHER: It's nice to see your face.
BRANDON: Yes.
Audio Description: And then counts to the right.
BRANDON: That would be 3, 5.
TEACHER: Okay. And you could double check that by doing the slope.
BRANDON: Right.
TEACHER: Okay.
TEACHER: Clear you board.