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.
THE BIG FOUR: 1) The slope formula (mother of all linear equation formulas) 2) Point-slope form (we use it to get to Slope-intercept Form) 3) Slope-Intercept Form (our golden ticket cuz we love to graph with it) 4) Standard Form (aka "Intercepts Form") Thumbs ready??!!
... AND MORE: 5) Parallel and Perpendicular Lines (negative reciprocals RULE!!) 6) Scatter Plots and Trend Lines (No LINE OF BEST FIT and I will not test you on the vocab of interpolation and extrapolation... so DO NOT worry about that!) 7) I will go "easy" on DIRECT VARIATION equations... for now, you simply need to recognize them as specific LINEAR EQUATIONS that pass thru the origin (0,0). 8) Section 5-8 (Absolute Value Equations) is EXCLUDED for now!!!
#5) RELATE [The height of a candle over time] is [the initial height] less [the amount in inches it burns down over time] DEFINE h is height in inches m is time in minutes 12 inches is the initial (time zero) height, therefore we should recognize that it is the y-intercept. The candle burned 4 inches in 15 minutes, so the rate of change is -4/30 which reduces to -2/15 WRITE h=f(m)=(-2/15)m + 12
#6) When the Farabaugh family leaves town on vacation, they put their dog Clarence in a kennel. The kennel charges $8 per day. In addition, there is a $15 fee for a mandatory flea bath (just one bath for the entire stay). RELATE – DEFINE – WRITE a. Draw a graph showing the cost of a stay that can last up to 2 weeks (14 days). b. Write an equation that relates the length of the stay with the cost. c. What is the significance of the y-intercept? RELATE [The cost of a kennel stay] equals [the initial flea bath] plus [the cost of a day]*[the number of days boarded] DEFINE c is the cost d is the number of days $15 is the flea bath, $8 is the cost per day WRITE c=f(d)= 8d + 15
The y-intercept in the graph represents the cost of the flea bath.
A tire dealer sells Supreme tires for $48 each and Prestige tires for $72 each. During one month, the combined sales for both tires totaled $13,824. RELATE – DEFINE – WRITE a. Write an equation that you can use to determine the possible combinations of THE NUMBER OF Supreme tires (x) and the Prestige tires (y) sold. b. Graph the equation in the coordinate plane. c. IN THE CONTEXT OF THIS PROBLEM, what is the meaning of the x- and y- intercepts on your graph.
RELATE [The total sales dollars of the tires] is [the number of Supreme tires sold]*[the price of a Supreme tire] plus [the number of Prestige tires sold]*[the price of a Prestige tire] DEFINE x is the number of Supreme tires sold y is the number of Prestige tires sold Total sales dollars is $13,824; The price of a Supreme tire is $48; The price of a Prestige tire is $72 WRITE 48x + 72y = 13,824
The x-intercept represents the possibility where ONLY Supreme tires were sold.
The y-intercept represents the possibility where ONLY Prestige tires were sold.
Mr chamberlain, can you please make a video about changing slope-intercerpt form into standard form with and without using integers; it's still a little confusing.
Your TARGET is Standard Form Ax + By = C where A, B, & C are integers...
OK, we gotsk two problems... 1) the x & y terms need to be on the same side (one way to look at this is that we are solving for the constant, i.e. C) AND 2) there's this nasty fractional coefficient (i.e. -2/3) hanging around...
First let's add (2/3)x to both sides... (2/3)x + y = -5
Some people want to multiply by the reciprocal here, in this case 3/2, BUT(T) THAT would leave us with (2/3)y, yes??
So, we need to multiply by the Lease Common Denominator, aka LCD, of 3... that will CLEAR the fraction and create nothing but INTEGERS!! YAY!!
Mult both sides by 3 and get 2x + 3y = -15
Therefore, we can say that the following three equations are EQUIVALENT:
Plain and simple: Direct Variation equations are linear functions (note that a vertical line does NOT qualify as a function) that pass thru the origin.
Said another way: Direct Variation equations are equations in slope-intercept form where b=0.
Mathematicians like to make a big deal about Direct Variation... they like to say things like "the value of y varies DIRECTLY with the value of x"... in other words like it's a big deal that there is no constant involved.
Mathematicians can be a little weird, ya know?
If you are asked to identify an equation as to whether or not it is a direct variation (someone may ask you that sometime soon, hint-hint), you gotsk to answer 2 simple questions: 1) Is it a linear function? 2) Does it pass thru (0,0) aka the origin?
If you answer YES to both questions, it are am be a Direct Variation situation!!
Hi Mr. C! So here is my explanation for problem 41 on page 350. First you have to convert the slope intercerpt form to standard form or the intercepts form. You do this by getting x and y on the same side because the formula for standard form is Ax+By=C (The equation is y=-4x+2) So, you have to add 4x to both sides to cancel out the -4x on the one side and add it to the "y side" if you will. So your equation should look like this; 4x+y=2. Then to get the x-intercept, you have divide both sides by 4 to get what x is (the x-intercept). So 2/4 is 1/2. So your x-intercept is 1/2!
You need to know the following for the test:
ReplyDeleteTHE BIG FOUR:
1) The slope formula (mother of all linear equation formulas)
2) Point-slope form (we use it to get to Slope-intercept Form)
3) Slope-Intercept Form (our golden ticket cuz we love to graph with it)
4) Standard Form (aka "Intercepts Form") Thumbs ready??!!
... AND MORE:
5) Parallel and Perpendicular Lines (negative reciprocals RULE!!)
6) Scatter Plots and Trend Lines (No LINE OF BEST FIT and I will not test you on the vocab of interpolation and extrapolation... so DO NOT worry about that!)
7) I will go "easy" on DIRECT VARIATION equations... for now, you simply need to recognize them as specific LINEAR EQUATIONS that pass thru the origin (0,0).
8) Section 5-8 (Absolute Value Equations) is EXCLUDED for now!!!
Capeesh?
Unit 5 Problem Set B ANSWERS!!
ReplyDelete5B #1-4 Please feel free to challenge me if you think I made a mistake or typo...
#1)
y = (-1/3)x - 6
-x + 3y = -18 OR
x - 3y = 18
#2)
y = -2x - 2
2x + y = -2
#3)
y = (1/6)x + 1
-x + 6y = 6
x - 6y = -6
#4)
y = (-6/5)x - (49/5)
6x + 5y = -49
#5)
ReplyDeleteRELATE [The height of a candle over time] is [the initial height] less [the amount in inches it burns down over time]
DEFINE
h is height in inches
m is time in minutes
12 inches is the initial (time zero) height, therefore we should recognize that it is the y-intercept. The candle burned 4 inches in 15 minutes, so the rate of change is -4/30 which reduces to -2/15
WRITE
h=f(m)=(-2/15)m + 12
#6) When the Farabaugh family leaves town on vacation, they put their dog Clarence in a kennel. The kennel charges $8 per day. In addition, there is a $15 fee for a mandatory flea bath (just one bath for the entire stay).
ReplyDeleteRELATE – DEFINE – WRITE
a. Draw a graph showing the cost of a stay that can last up to 2 weeks (14 days).
b. Write an equation that relates the length of the stay with the cost.
c. What is the significance of the y-intercept?
RELATE
[The cost of a kennel stay] equals [the initial flea bath] plus [the cost of a day]*[the number of days boarded]
DEFINE
c is the cost
d is the number of days
$15 is the flea bath, $8 is the cost per day
WRITE
c=f(d)= 8d + 15
The y-intercept in the graph represents the cost of the flea bath.
A tire dealer sells Supreme tires for $48 each and Prestige tires for $72 each. During one month, the combined sales for both tires totaled $13,824.
ReplyDeleteRELATE – DEFINE – WRITE
a. Write an equation that you can use to determine the possible combinations of THE NUMBER OF Supreme tires (x) and the Prestige tires (y) sold.
b. Graph the equation in the coordinate plane.
c. IN THE CONTEXT OF THIS PROBLEM, what is the meaning of the x- and y- intercepts on your graph.
RELATE
[The total sales dollars of the tires] is [the number of Supreme tires sold]*[the price of a Supreme tire] plus [the number of Prestige tires sold]*[the price of a Prestige tire]
DEFINE
x is the number of Supreme tires sold
y is the number of Prestige tires sold
Total sales dollars is $13,824; The price of a Supreme tire is $48; The price of a Prestige tire is $72
WRITE
48x + 72y = 13,824
The x-intercept represents the possibility where ONLY Supreme tires were sold.
The y-intercept represents the possibility where ONLY Prestige tires were sold.
Mr chamberlain, can you please make a video about changing slope-intercerpt form into standard form with and without using integers; it's still a little confusing.
ReplyDeleteNo time for a video tonight...
Deletelet's say you have:
y = (-2/3)x - 5
Your TARGET is Standard Form Ax + By = C
where A, B, & C are integers...
OK, we gotsk two problems...
1) the x & y terms need to be on the same side (one way to look at this is that we are solving for the constant, i.e. C) AND
2) there's this nasty fractional coefficient (i.e. -2/3) hanging around...
First let's add (2/3)x to both sides...
(2/3)x + y = -5
Some people want to multiply by the reciprocal here, in this case 3/2, BUT(T) THAT would leave us with (2/3)y, yes??
So, we need to multiply by the Lease Common Denominator, aka LCD, of 3... that will CLEAR the fraction and create nothing but INTEGERS!! YAY!!
Mult both sides by 3 and get
2x + 3y = -15
Therefore, we can say that the following three equations are EQUIVALENT:
y = (-2/3)x - 5
2x + 3y = -15
Capeesh?
Can you explain direct variation?
ReplyDeletePlain and simple: Direct Variation equations are linear functions (note that a vertical line does NOT qualify as a function) that pass thru the origin.
ReplyDeleteSaid another way: Direct Variation equations are equations in slope-intercept form where b=0.
Mathematicians like to make a big deal about Direct Variation... they like to say things like "the value of y varies DIRECTLY with the value of x"... in other words like it's a big deal that there is no constant involved.
Mathematicians can be a little weird, ya know?
If you are asked to identify an equation as to whether or not it is a direct variation (someone may ask you that sometime soon, hint-hint), you gotsk to answer 2 simple questions:
1) Is it a linear function?
2) Does it pass thru (0,0) aka the origin?
If you answer YES to both questions, it are am be a Direct Variation situation!!
Capeesh?
is there any homework due nxt class???
ReplyDeleteHi Mr. C! So here is my explanation for problem 41 on page 350. First you have to convert the slope intercerpt form to standard form or the intercepts form. You do this by getting x and y on the same side because the formula for standard form is Ax+By=C (The equation is y=-4x+2) So, you have to add 4x to both sides to cancel out the -4x on the one side and add it to the "y side" if you will. So your equation should look like this; 4x+y=2. Then to get the x-intercept, you have divide both sides by 4 to get what x is (the x-intercept). So 2/4 is 1/2. So your x-intercept is 1/2!
ReplyDeleteMr.c
ReplyDeleteThere is no problems 50-55 on page 346 what are the correct homework pages and numbers
NO HOMEWORK... CONGA-LINE!!! WOO-HOO!!
ReplyDelete