Project Math Access DVD 03 - Algebra - Part 08
Transcript Start
Audio Description: Part eight; solving equations using graphing; example two.
TEACHER: Alright, how about number 4?
BRANDON: Okay.
Audio Description: Brandon reads the braille sheet.
BRANDON: Number 4. Write the equation of the line through A and B.
TEACHER: The line that passes through A and B. If you were to plot points A and B and put the line on there... Why don't we do it on the graph paper, just so we have it. A little visual.
BRANDON: Okay.
TEACHER: Point A was negative 3, 5.
BRANDON: Negative 3, 5.
BRANDON: So that would be... So again, we start from the origin. Always start from the origin.
TEACHER: Yes.
BRANDON: That is important to remember.
TEACHER: Great.
TEACHER: Plot the point.
BRANDON: So, negative 3, 5... So, X comma Y So that means we go to the left 3, and up 5. 1, 2, 3,4, 5. So we take off a point, and put it down there.
TEACHER: And then, B was negative 1, negative 3.
BRANDON: Now we start from the origin again.
TEACHER: Okay.
BRANDON: So... now we need to go negative 1, negative 3. So we go to the left 1, and down 3 And then we take a point off of the... And then we... put it down. Now also on the graphing board here, you will see two Wikki Stix Now, the Wikki Stix are what we use to connect the points.
TEACHER: Kind of like connecting the dots.
BRANDON: Yes. Connect the dots, connect the points.
TEACHER: There you go. Pick a Wikki Stix.
BRANDON: Yes, pick a Wikki Stix.
BRANDON: You put it down...
TEACHER: It's still stuck on the other one.
BRANDON: You want to make sure the Wikki Stix is straight.
TEACHER: How can you do that?
BRANDON: You pull the two ends.
TEACHER: Right.
BRANDON: Pull it by both ends.
TEACHER: Pull it taut.
BRANDON: Pull it taut. Now,... now... To make the line going through the points, it has to... the Wikki Stix has to be right on both of the points. So... we're going to put in on both points
TEACHER: Lay it across the points.
BRANDON: Yes, and to make sure it's straight... Now the way you can tell if it's not straight is when you have it over the points and it's wavy on the ends.
TEACHER: Right, or you can also use a ruler and line it up against that. We've done it a couple of times.
BRANDON: But I don't particularly like that method.
TEACHER: Well, I'm sorry.
BRANDON: Oh well.
TEACHER: Okay, so let's see. Lift up. Pretty good, but your end is a little crooked. When you're laying it down, make sure you're keeping it taut, and hold it from either end, and lay it down. Use your other finger to find the points.
BRANDON: Okay.
TEACHER: Good.
TEACHER: Looks good. Alright, so we have our line. No, leave it there. We need the visual. Let me fix that, just a little bit. One of your points is actually a double point, here.
BRANDON: A double point? (laughs)
TEACHER: So, I'm going to pull that apart 1 was negative 1, negative 3.
Audio Description: The teacher replaces the point and straightens the Wikki Stix.
TEACHER: Alright. Good. Feel it now, it's all straight.
BRANDON: Yes.
TEACHER: Okay?
BRANDON: Yes.
TEACHER: Now, we're going to write the equation of the line that passes through A and B. Do you remember how to write the equation?
BRANDON: Yes.
TEACHER: Okay.
BRANDON: So... Hmmmm.
So Y...
Oh, Oh. We use either one for X Y.
TEACHER: Sure.
BRANDON: So... so... let's see...
Audio Description: Brandon checks his braille sheet.
TEACHER: First of all, do you have number 4 labeled on your brailler?
BRANDON: Yes I do.
TEACHER: Great.
BRANDON: Now, the formula for equations of the line... is Y minus... How do you say this?
TEACHER: I don't know.
BRANDON: Y... sub 1?
BRANDON: How should we say this?
TEACHER: Y minus Y sub 1? Is that how you want it?
BRANDON: Yeah, but I'm not sure they know that means.
TEACHER: Well, sub 1 is your first point.
BRANDON: Okay. Oh, a better way to put it, simpler terms Y minus the Y coordinate... equals... slope... open parenthesis, X minus the X coordinate. Close parenthesis.
TEACHER: So essentially, it turns into Y-Ysub1=M(X-Xsub1)
TEACHER: Good, okay. So, let's plug in the terms.
BRANDON: So, we're going to have Y minus 5
TEACHER: Okay.
BRANDON: Equals...
Audio Description: Brandon refers to what he as already written on the braillewriter.
BRANDON: Negative 4.
TEACHER: Okay.
BRANDON: Open parenthesis, X...
Audio Description: Brandon refers to the problem on the braille sheet.
BRANDON: Now, since it's X minus a negative 3 we simply put X plus 3.
TEACHER: Right, because a negative plus a negative is a positive.
BRANDON: ...plus 3, close parenthesis.
TEACHER: So what you should have is Y minus 5 equals -4, open parenthesis, X plus 3, close parenthesis
BRANDON: Check.
TEACHER: Good.
BRANDON: So... now what we want to do we want to get this into the equation of the line format the formula, Y = mX + B
TEACHER: Which is...
BRANDON: M being the slope, and B being the Y intercept. This is also called "slope intercept" form.
TEACHER: Good.
BRANDON: Okay. First thing we want to do is, we want to... fix... fix... the fixed... fix the right side of the equals sign.
TEACHER: So you're going to take care of your order of operations and do the parentheses first.
BRANDON: Right, and we need to distribute.
TEACHER: Distribute that negative 4 into those parentheses.
BRANDON: So Y minus 5... equals... negative 4x minus 12. Okay.
TEACHER: Good.
TEACHER: Okay, now what?
BRANDON: Now we can add 5...
TEACHER: Why?
BRANDON: Ummm... we need to get this into the proper form.
TEACHER: Because the Y doesn't like hanging out with anyone else.
BRANDON: Right.
TEACHER: He wants to be by himself.
BRANDON: He's not social.
TEACHER: That's right.
BRANDON: He doesn't have any social skills.
TEACHER: We going to get him by himself. So add the 5 to the other side.
BRANDON: Yes, so Y equals... minus 4x minus 7
TEACHER: Good.
BRANDON: Now, this is what we call the slope intercept form. Which we said earlier was Y=mX+B. So m is the slope, and B is the Y intercept so that means the slope is negative 4 and the Y intercept is negative 7
TEACHER: Which leads very nicely to the next question which says use your equation to graph the line through A and B. We already graphed the lines, so now you have your equation you can see if your graph is correct by checking the Y intercept and the slope.
Audio Description: Brandon checks the tactile graph.
TEACHER: So what's your Y intercept again?
BRANDON: It is negative 7.
TEACHER: So, see if the line goes through negative 7.
BRANDON: Here's 7 on the Y.
TEACHER: Uh, hmmm. Start at the origin, and it's negative 7.
BRANDON: Oh... duoh!
TEACHER: Alright, so you want to go down...
BRANDON: So you start at the origin and we go down 7,
BRANDON: 1, 2, 3,...
TEACHER: Don't go too fast.
BRANDON: Starting at the origin, 1, 2, 3, 4, 5, 6, 7.
BRANDON: There we go.
TEACHER: The line goes through it?
BRANDON: Yep.
TEACHER: Now, your slope was negative 4
BRANDON: Negative 4...
TEACHER: So, how do we figure that?
BRANDON: ...back at the origin...
TEACHER: Nope.
TEACHER: Start from your Y intercept.
BRANDON: Oh, shoot.
TEACHER: That's alright. You're at negative 7
BRANDON: Negative 7...
TEACHER: So what is slope?
BRANDON: Slope is rise over run...
TEACHER: Right.
TEACHER: So you need to... What's rise? Negative...
BRANDON: Negative 4.
TEACHER: Actually, let's just make the slope 4, and then make the run negative 1. Because our line doesn't go down that far, to go down.
BRANDON: Right. So, 4
TEACHER: So, you'd go up...
BRANDON: ...2, 3, 4,...
TEACHER: and over negative 1.
BRANDON: And there it is.
TEACHER: There you go. So, was your line correct?
BRANDON: Yep.
TEACHER: Good job. Excellent work.