hw#5-7: Due Thurs Jan 20th
HOMEWORK
SMORGASBORD!!
pg 338-39 #9,10,18,19
For the UNIT TEST, you should IMMERSE yourself in pages 348-353. You don't have do to every problem, but YOU DO HAVE TO KNOW HOW TO DO EVERY PROBLEM!!
AND, you should know where to ask questions if you need help.
For those so inclined, now would be a good time to look at pages 354-356... it's a GOOD START for the mid-term review.
do u know when we have to take the midterm review
ReplyDeleteYou can do the mid-term review 24x7, WOO-HOO!!! Let me know if you run out of problems, I have an infinite supply!!!
ReplyDeleteOh... I suppose you meant to ask "When is the mid-term EXAM?"
I don't have a date yet... it will very likely be sometime during the week of Jan 24-28th.
Someone worked on the Extra Practice packet (found on Mathchamber Unit 5 as a link at the bottom of the page) and had trouble with #25, 54, & 60c.
ReplyDeleteSo here is the help:
#25) Find the slope and y-intercept of 4x–5y=2
Ans: Convert to slope-intercept form
4x–5y=2 (sub 4x fbs)
-5y=-4x+2 (dbs by -5)
y=(4/5)x - 2/5
Slope: 4/5 y-int: (0,-2/5)
#54) Write an equation in standard form that satisfies the given conditions:
Perpendicular to 4x+3y=12 and through (7,1)
Wow-zers... what a GREAT PROBLEM... you gotsk to understand a lot here.
General explanation: You need to find the slope of the given line, use the opposite reciprocal to find the slope of the target line, and then use point-slope form to find slope-intercept form of the target line and then convert back to standard form. Tons of algebra FUN!!
Slope of the given line is -A/B or -3/4 (you could also convert to slope-intercept form).
OppRecip = 4/3, right?
Use Pt-Slp form with m=4/3 (7,1):
y-1=(4/3)(x-7)
y-1=(4/3)x-28/3
y=(4/3)x-25/3
Now, convert to standard form (w/ int coefficients)
-(4/3)x+y=-25/3 (mbs -3)
4x-3y=25
ta-dah!!!!
#60c) (You'll have to look at the problem)
We did NOT work on lines of best fit (which require a graphing calculator - that's a coming attraction!!). However, you should have been able to "rough sketch" a TREND LINE with a slope somewhere between 2/3 and 3/4 (.66 and .75) and a y-intercept of approximately -1.
lmk if all of this helped!!
Mr. C.
For #5, in the textbook on pg 349, would that be the line of best fit? (Which we aren't doing)
ReplyDeleteFor scatter plots, are you allowed to put a break (that squiggly thingie) on the x-axis also if you want to skip a few numbers?
ReplyDeleteYes, and since we aren't DOING IT, you should KNOW IT. The trend line is an approximate line that we draw and then estimate an equation. It's best to use round numbers (i.e. 1/2 instead of .512, etc.). The line of best fit will yield a more precise solution, based on the data input into the algorithm (or graphing calculator). Always remember that the line of best fit is used to MODEL and ESTIMATE a "scattered" real-life situation. For many real-life situations, your ability to estimate a trend-line will be close enough.
ReplyDeleteI keep forgetting.. How do you find an equation for a trend line?
ReplyDeleteA good idea for today would be to visit the MathChamber Unit 5 page and look at the Extra Practice worksheet (bottom of page). An answer key is included for your reference.
ReplyDeleteIf you have the Unit 5 test nailed, why not start on the mid-term review exercises?
Wait-- Do you find a point on the line & then find the slope using the points, & then plug in the slope into y=mx+b?
ReplyDeleteHow would you find the y-intercept? Is it where the trend line begins or horizontal from the point you picked to find the slope?
how do you find the y-intercept in a scatter plot to find an equation
ReplyDeleteYou draw the trend line as best you can. You can simply guess-timate the equation by estimating a slope and a y-intercept OR you can be a bit more precise and pick two points - remember to pick points on your line, which aren't necessarily actual data points - and then find the slope, and then use point-slope form to get you to slope-intercept form.
ReplyDeleteWhen you are asked to write an equation for a line, you should always choose either slope-intercept or standard form as a "target" - point-slope form is a "vehicle" to get you there... ca-peesh??
If the trend line you draw doesn't extend to the y-axis, you must EXTRAPOLATE by extending the line along the same slope!! Moving horizontally would negate the trend, yes??
Oh now I got it.
ReplyDeleteYES!!
Watch the video tutor on MathChamber...
ReplyDeletehttp://www.pearsonsuccessnet.com/content/HVT_English/academy123_content/wl-book-demo/ph-921s.html
and lmk if you still have questions... k?
For the "Using scatter plots and trend lines to make predictions" video tutor problem, what could you estimate as an equation in slope-intercept form? Go ahead, give it a try!
ReplyDeleteI'll try! I have to watch it again.. Since you can't fast forward through those videos! Hold on a minute :)
ReplyDeleteUm.. I got
ReplyDeletey=12/25x+90 2/5
Are you allowed to use breaks in x axes?
ReplyDeleteWhy would ANYONE fast forward through a math video?! Don't you just wanna sit back and BASK in the mathematical sunshine?!
ReplyDeleteThe y-intercept is hovering around 10 or so, right? For the slope, you should pick two point as far apart as possible... I see (0, 10) and (200,100). So I see a slope of 90/200 which reduces to 9/20 or .45, right?
So now I gotsk a slope and a y-intercept:
y = .45x + 10
Can you describe what this equation means in real-life terms?
Caution: It does not mean that a tree with a circumference of zero is 10 feet tall... how can you explain this anomaly?
If you were using integer coefficients on #5 in the Chapter Test, would the correct answer be 3x-4y=-20?
ReplyDeleteUh.. The height of the tree is .45 times the circumference plus 10?
ReplyDeleteWould #8 be a horizontal line? Yes?
ReplyDelete(In the Chapter Test)
Dear Last3,
ReplyDeleteYup, Yup, and Yup!!
Mr. C.
Need help on the direct variation questions #11 & #12.
ReplyDeleteI'm trying to get #11 into the equation y=kx. Right now I have 3y=-2x. Am I on the right path? Should I divide 3y & -2x by 3?
Confused on 15 b. on the Chap. Test. Wouldn't the x & y intercepts be (0,0)?
ReplyDeleteDear #11,
ReplyDeleteGiven that your target is y=kx, what's the matter with 3y=-2x? The three, right? What's it doing to y? How do you UNDO that?
For the next step, you need to EXTRACT the numeric part of the term, so that you have a distinct value for k. if you had 12x/13 you would extract 12/13 so that you would have (12/13)x, right?
lmk if this helped and try #12 on your own.
For #15, the x- and y- intercepts would only be (0,0) if the line went through the origin. In this problem, the $35 spent on supplies seems to be a cost incurred even if no pets are groomed. What does that mean for your line?
There is a certain type of line we learned about in this unit that has an x- and y- intercept of (0,0). Do you know the name for this type of linear equation????
Fill in the blanks:
ReplyDeleteA graph of the line for a ________ variation equation always includes the point (___,____), a.k.a. the __________.
A direct variation equation can be written as
ReplyDeletey = __x
or
y/x = ____
where ___ is a _______ _________.
Is #11 y=-2/3x?
ReplyDeleteAnd #12 does not represent a direct variation..
???
Oh I forgot about that $35..
Would the y-intercept then be -35? And the x-intercept be 8?
I don't know about the first on..
ReplyDeletey=kx
or
y/x=k
Where k is real number?
Yup, y = (2/3)x, (not 2 over 3x)
ReplyDeleteA graph of the line for a DIRECT variation equation always includes the point (0,0), a.k.a. the ORIGIN.
For #11, it was $30 (I didn't have my glasses on) but otherwise yup for 11 & 12.
What does the x-intercept tell you in that graph?
I'm goin' ice fishin'... see you later!
Am I doing something wrong on #16?
ReplyDeleteMy equation for the line turned out to be:
y=-2000x+40,024,000
D:
Oops.. Well then for #11 I already used $35 to make the graph......
ReplyDeleteOkay.. I think I will resume asking questions tomorrow then.
ReplyDeleteHave fun :)
For #16, just answer the question. I know it's a lot of fun to write equations and solve and simplify, but they just wanted to know how many inventors had applied for patents in a given year. JUST ANSWER THE QUESTION!
ReplyDeleteThey did not ask for an equation, so you don't need to provide one.
If you simply made a graph (even without a graph) you could see that the number of inventors applying for patents decreased by an average of (very) roughly 1,000 per year. You can interpolate to get the number in 2006 and extrapolate to estimate a number for 2015.
Had you been asked to provide an equation, one technique often employed is to set the starting year to 0, in this case 1999=0. It just makes it easier to "do the math" that way.
when the you find a slope...and it equals 0/4...is that 0 or undefined, and vice versa (4/0)
ReplyDeleteNot to worry for #11, as long as you understand the concept.
ReplyDelete0/4 or 0/(any real#) equals zero. Zero is a number. It qualifies as a slope. It is the slope of a horizontal line.
ReplyDelete4/0 or (any real#)/0 does not yield a number. Zero does not go into 4 (or any number) any number of times. It cannot be done. Therefore, we label this ratio as UNDEFINED. The slope ratio presents us with a denominator of zero when applied to a vertical line. Therefore, the slope of a vertical line is UNDEFINED.
I warned all of you two months ago that horizontal and vertical lines would haunt you. You see what I mean now, huh?
Mathematicians sometimes argue about 0/0 (it's often a hot topic at Friday night Math Parties!). Is it a number or undefined OR is it BIG FAT ONE since any number over itself is ONE?
See part of the debate here:
http://www.newton.dep.anl.gov/askasci/math99/math99259.htm
For our purposes, we'll go with the prevailing logic that 0/0 is undefined. Fortunately, that will not affect our calculations of slope, so we can ignore the debate for now.
Mr. C.
For #16, I thought I needed to find the equation so I could extrapolate & not need to extend the graph.. So I could use the equation to figure that out?
ReplyDeleteHelpful? Yes. Needed? Not unless it's asked for... if you can see the pattern, just use it. The slope isn't much more than a pattern, right?
ReplyDeleteDid you see what I meant about setting the starting year to zero. The y-intercept of 40 million is kinda useless. Also, your slope should have been -1,000, not -2,000, due to the fact that the data table was for odd years only.
Ca-peesh?
Got it! And also.. I'm still confused. The opposite reciprocal of x would be -(1/x), right? Because -(1/x)*x/1=-(x/x)=-1
ReplyDeleteWait.. Will that be on the test? Because I keep thinking that -x is the slope.. Although the slope of -x is -1.
ReplyDeleteIs it true that..?
ReplyDelete...when the absolute value equation is y=|x|, then adding will move the graph of the equation up the y axis and subtracting will move the graph of the equation down the y axis.
...when the absolute value equation is y=|x+/-__| (subtracting or adding inside the absolute value symbols) then adding will move the graph of the equation to the left (or negative direction) on the x axis and subtracting will move the graph of the equation to the right (or positive direction) on the x axis.
?????
OF COURSE IT WILL BE ON THE TEST!!!
ReplyDeleteThe slope IS the coefficient. You explained it perfectly!!
OK!!!!
ReplyDeleteAnd yay! :))
Dear ABSVAL Transformer,
ReplyDeleteYou got it... in your first paragraph you forgot to specify "outside" the ABSVAL brackets, but I know you meant to!
Of course, you also mean adding or subtracting positive numbers. If you were you to add a negative number, that would be the same as subtracting a positive... but you understand that, too (I think).
And if you want to be a TRUE algebraic transformer, you would say "translate" (the slide transformation) instead of "move."
Ca-peesh?!
(I understand)
ReplyDeleteCa-Peesh!
Because #22 on the chapter test is about line of best fit, will we have to know about it?
ReplyDeleteFOR THE LAST TIME... you will be asked to work with trend lines... you should now that a line of best fit can be generated, but you will not be asked to do it.
ReplyDeleteSo read the note below and be ready to generate a trend line:
To generate a line of best fit requires a fairly tedious and complex algorithm, which you will learn in later years in a Statistics class (perhaps at MHS, perhaps in college). The input consists of all of the ordered pairs in the data set. To generate a line of best fit, you don't even have to draw a graph, you just manipulate the the data using the algorithm, and, just like that, out pops a linear equation in slope-intercept form. We will actually do this later in the year... you'll see that a graphing calculator takes all the hard work (aka FUN) out of the tedious and complex algorithm.
Correlation coefficients are another output from the algorithm. A correlation coefficient of 1 shows a perfect (every data point is on the line) positive correlation and a correlation coefficient of -1 shows a perfect negative correlation. As correlation coefficients get closer to 0, that indicates that the a weaker "fit" of the data to the line. FOR UNIT 5, YOU WILL NOT BE RESPONSIBLE FOR CORRELATION COEFFICIENTS (beware your algebraic crystal ball). Statisticians use terms like "strong correlation" or "weak correlation" to recognize how well a data set is represented by a line of best fit.
As an alternative CALCULATING a line of best fit, you can graph the ordered pairs as a scatter plot, and draw (estimate) a trend line through the data. This line can then be fitted with a slope and y-intercept using all of the skills you learned in this unit. Once again, your output is a linear equation in slope-intercept form. It just wasn't generated as precisely as the line of best fit algorithm.
OK, I'm exhausted now... I hope that answers your question.
please use the next post if you have more questions... I'm tired of scrolling!
ReplyDeleteThank you! I got it!
ReplyDeleteSorry I posted so much..