fyi... For those so inclined, now would be a good time to look at pages 358-360... it's a GOOD START for the mid-term review. Tentative Mid-Term date is Tuesday Jan 31 (B), Wed Feb 1 (A).
Due Mon Jan 23 (B)
Tue Jan 24 (A)
Complete Unit 5 Problem Set A
Note to Absentees!! This Problem Set is a printable pdf file... you are expected to complete it... see your friends or me for help
PROBLEM SET 5A WILL BE COLLECTED AND GRADED!!
Optional Additional HW:
(for those that prefer A's to those other grades):
pg 326
#27-30 Graph all 4 lines on ONE coordinate plane
#37,40,41,43
#45,47 (Hint: to use the graphing calculator, you'll have to convert to slope-intercept form)
ALSO: Browse the Mid-Chapter Review (pg 321)... you should feel comfortable with all of those problems, EXCEPT FOR #7-9... add #26 to your assignment (above) for EXTRA CREDIT!!)
some of you asked about pg319/#27 from the previous hw assignment...
ReplyDeleteIn #27, you are told the relationship is linear and you are given two points. We are asked to find the Celsius temp given the Fahrenheit temp, so we will say that the Celsius temp depends on the Fahrenheit temp, SO, C is the dependent and F is the independent variable.
Therefore, we have the points (50,10) and (77,25), agreed?
Can you calculate the slope? SURE!!!
The slope is 15/27, which simplifies to 5/9, yes?
NOW, we can use point-slope form to derive slope-intercept form, yes?
So:
y-y1=m(x-x1)
y-10=(5/9)(x-50)
y-10=(5/9)x - (250/9)
y-(90/9)=(5/9)x - (250/9)
y=f(x)=(5/9)x - (160/9)
Slope is 5/9 and y-intercept = -160/9
So, now we can substitute ANY Fahrenheit temp and obtain a Celsius temp.
Gosh, we end up with an f of F... how about that??
C=f(F)=(5/9)(59) - 160/9
C = 295/9 - 160/9
C = 135/9 (how many times does 9 go into 135??)
C = 15
So, when the temp is 59F it is 15C... Brrrrrrr!!
Capeesh?
someone in the 7th grade class asked about the thumb cover up method...
ReplyDeleteWhen a linear equation is in standard form, you can use the "Intercepts Method" (aka Thumb cover-up) to determine the x- and y- intercepts, thus finding two points in the coordinate plane, which will allow you to sketch your line. We briefly discussed this in our last class.
For example, let's say you are asked to graph the equation 2x + 3y = 6 in the coordinate plane. Due to your extremely high level of algebraic training, you immediately recognize that this equation is in standard form for a linear equation (brilliant!). All you need to do now is identify two ordered pair solutions (aka points), and you gotsk your line.
The value of the x-coordinate for the y-intercept will always be zero. The value of the y-coordinate for the x-intercept will always be zero. These two sentences are borderline tongue-twisters... but graph a few examples and I think you'll agree.
If we substitute zero for x we get
2(0) + 3y = 6
0 + 3y = 6
3y = 6
y = 2
When x=0, y=2, so the y-intercept is (0,2)
When we substituted zero for x, it is as if the 2x term was "covered up" yes?
If we substitute zero for y we get
2x + 3(0) = 6
2x + 0 = 6
2x = 6
x = 3
When y=0, x=3, so the x-intercept is (3,0)
When we substituted zero for y, it is as if the 3y term was "covered up" yes?
In summary, we have an easy method to find the intercepts when a linear equation is in standard form (which we also called "Intercepts Form"). The nickname for this method is the "thumb cover-up" method, because when you substitute zero for either variable, it is as if you are covering that term with your thumb.
Thumbs up?
Mr. C.
would you rather see the y-intercept form written with a fraction slope, or as a decimal slope.
ReplyDelete~~~~~~~> y=-7/2x+5 (or) y=-3.5x+5 which one do you prefer?
That's a very good question.
DeleteIf the question is just "naked algebra" and it starts with integers, you should use fractions, and leave them as improper.
If the problem is s word problem that "lends itself" to decimals (i.e. a money problem) you can use decimals.
When in doubt, unless there is a compelling reason to use decimals, you should stick with fractions. As you move up the mathematical ladder thru HS & College, fractions will generally be more useful and workable.
I will not mark either answer above incorrectly, UNLESS I specifically ask for the answer to remain in one form or another.
Thanks for asking!!
thanx for answering
ReplyDeleteEVERYBODY PLAY THIS MATH GAME AND LISTEN TO THE MUSIC
ReplyDeletehttp://hotmath.com/hotmath_help/games/kp/Karappan_Poochi_Sound.swf
In the packet i'm confused with slop formula. When i get an answer for m= and draw a line the line doesn't match up with the points that are in the problem any advise or is there a mistake i'm making?
ReplyDeleteSo i want to make sure I'm doing this right. Lets say on #4 a i got my answer which was y= 4-3/2x. is that slope negitive that i would place the dot in the negitive part of the corridante plain?
DeleteIF you have y = 4 - (3/2)x you have written your equation in "intercept-slope form" (the difference in order is ok AND important).
DeleteYou could have also written:
y = -(3/2)x + 4
That means a y-intercept of +4 (aka (0,4)) and the line should have a negative slope (i.e. RISE -3, then RUN +2).
Capeesh?
I need help with #5 d. how do you work with the undefined number?
ReplyDeleteAn undefined SITUATION is NOT A NUMBER!
ReplyDelete5 divided by 0 (or 10/0 OR -32/0) cannot happen. WE WILL DISCUSS IN CLASS ONE MORE TIME TODAY!!