This Blog exists for the collective benefit of all algebra students. While the posts are specific to Mr. Chamberlain's class, any and all "algebra-ticians" are welcome. The more specific your question (including your own attempts to answer it) the better.
A direct variation equation is SIMPLY a slope-intercept form equation where the value of 'b' = zero. If a linear function is identified as a DIRECT VARIATION, that means that it passes through the point (0,0).
So if y=-4 when x=4, that means that one point on the line is (4,-4), right?
If we are told that this is a DIRECT VARIATION, that means that (0,0) is ALSO a point on the line.
Can you draw a line through (4,-4) and (0,0)?? (I think you can!!!!)
Can you tell me the slope of that line? The y-intercept should be a duh!, yes?
I think that (with what you know so far) #8 is a very difficult problem... with what we learn in class tomorrow it will become MUCH easier... will you allow me to hold off until tomorrow??... betcha can't wait for class now, eh?
Standard Form requires the variables to be on the same side (left is best) and the coefficients and the remaining constant to be INTEGERS.
You can do the following steps in either order. Most algebra-ticians will "move" the variables to the same side first, in this case subtract (1/4)x from both sides to obtain:
(-1/4)x + y = -3
We're almost there. We gotsk to get rid of that fractional coefficient... we'll do that by multiplying both sides by the least common denominator (LCD), which in this case is the only denominator, 4:
-x + 4y = -12
The final "pretty" step is actually optional in my class... some (nasty) algebra teachers require the coefficient of x to be positive, which would force you to distribute a -1 to both sides, obtaining:
x - 4y = 12
For a check, graph the original slope-intercept equation and the new standard form equation (using "thumb cover-up") and you should find that you are graphing the same line!
Questions nearly identical to these will be on Thursday "Mea Culpa" Test (look it up!)
ReplyDeletepg 68-72 #29,55,71,81
pg 152-56 #17,49
pg 222-26 #15,35,43,45
pg 283-86 #19,20,21,23
pg 353-56 #9,15,19,25,27,29,31
Mea culpa means my fault!!!
ReplyDeleteI need some help on pg 354 with question 15. i dont understand how to write a direct variation equation.
ReplyDeleteA direct variation equation is SIMPLY a slope-intercept form equation where the value of 'b' = zero. If a linear function is identified as a DIRECT VARIATION, that means that it passes through the point (0,0).
DeleteSo if y=-4 when x=4, that means that one point on the line is (4,-4), right?
If we are told that this is a DIRECT VARIATION, that means that (0,0) is ALSO a point on the line.
Can you draw a line through (4,-4) and (0,0)?? (I think you can!!!!)
Can you tell me the slope of that line? The y-intercept should be a duh!, yes?
Capeesh?
On the hw i dont understand how to do #8. i think im having a brain fart at the moment
ReplyDeleteI think that (with what you know so far) #8 is a very difficult problem... with what we learn in class tomorrow it will become MUCH easier... will you allow me to hold off until tomorrow??... betcha can't wait for class now, eh?
DeleteI agree with mr or mrs. brain fart I could do number 7 but * is giving me trouble.
ReplyDeletewhen is the mea culpa test?
ReplyDeletefor direct variation since the b=0 would the answer be whatever the ordered pair is?
ReplyDeletecan you explain again how to turn clope intersept form in to standard? im still a bit fuzzy on that...
ReplyDeleteLet's say you have y=(1/4)x - 3
DeleteStandard Form requires the variables to be on the same side (left is best) and the coefficients and the remaining constant to be INTEGERS.
You can do the following steps in either order. Most algebra-ticians will "move" the variables to the same side first, in this case subtract (1/4)x from both sides to obtain:
(-1/4)x + y = -3
We're almost there. We gotsk to get rid of that fractional coefficient... we'll do that by multiplying both sides by the least common denominator (LCD), which in this case is the only denominator, 4:
-x + 4y = -12
The final "pretty" step is actually optional in my class... some (nasty) algebra teachers require the coefficient of x to be positive, which would force you to distribute a -1 to both sides, obtaining:
x - 4y = 12
For a check, graph the original slope-intercept equation and the new standard form equation (using "thumb cover-up") and you should find that you are graphing the same line!
Capeesh??
okay i finally get this clearly thank you
DeleteIm confused on how reciprocals work, any help explaining them?
ReplyDeleteA reciprocal of a number is the number which "partners" with the original number to create a product of 1.
ReplyDeleteThe reciprocal of 2 is 1/2.
The reciprocal of 1/3 is 3/1 or 3.
The reciprocal of -1/4 is -4/1 or -4.
We have learned that perpendicular lines have slopes that are NEGATIVE (or OPPOSITE) reciprocals of one another.
See this link for a fresh look:
http://regentsprep.org/Regents/math/ALGEBRA/AC3/Lparallel.htm
Mr. C.