anonymous
  • anonymous
The equation y = 16x + 560 describes the number of calories in a recipe, where y is the total number of calories and x is the number of teaspoons of sugar added. The table shows the number of calories in another recipe, where y is the total number of calories and x is the number of teaspoons of honey added. How many calories are in a teaspoon of sugar, and how many are in a teaspoon of honey?
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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anonymous
  • anonymous
i think the tablespoon of sugar is 576, but what is the tablespoon of honey plz help?
anonymous
  • anonymous
@dan815 @sleepyjess @just_one_last_goodbye @SolomonZelman @KendrickLamar2014

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anonymous
  • anonymous
i meant teaspoon not tablespoon my bad
anonymous
  • anonymous
Hi there!
anonymous
  • anonymous
hi may you plz help?
anonymous
  • anonymous
This is the equation for sugar. y = 16x + 560 To find out how many calories 1 teaspoon of sugar has, plug in x = 1 and solve for y.
whpalmer4
  • whpalmer4
\[ y = 16x + 560\]gives you the number of calories in a recipe where \(x\) is the number of teaspoons of sugar You also have a table showing the number of calories in another recipe where the number of teaspoons of honey is the independent variable. From these two, you can find how many more calories are added for each type of sweetener by looking at the slope of the function (or the line going through the data in the table).
anonymous
  • anonymous
ok
whpalmer4
  • whpalmer4
@TheSmartOne that won't work — you will include all the calories from OTHER ingredients as well. If you want to do it that way, you need to find the value of the calories for two recipes, subtract them and divide by the number of teaspoons used — finding the slope, in other words. But you can simply read that off the equation, too.
anonymous
  • anonymous
for the teaspoon of sugar i got 576, was that correct? if not, i will need some extra help
anonymous
  • anonymous
576 calories i mean
anonymous
  • anonymous
@whpalmer4 The question states that the honey and sugar are in two different recipes. Ah, nevermind. I see what you're saying! The slope is how many calories that the sugar has, and the slope obtained from the table tells us how many calories honey has.
anonymous
  • anonymous
@Houdini_Dragon Nevermind, what I said earlier. y = 16x + 560 That is the equation for the sugar. Can you tell me what the slope of the line is?
anonymous
  • anonymous
@TheSmartOne the slope is 16
anonymous
  • anonymous
now what?
anonymous
  • anonymous
So, in a recipe that has sugar there are 560 calories and depending on how much of sugar you put in, the calories will increase by 16 for each teaspoon of sugar added.
anonymous
  • anonymous
which is 576 correct? so i am right for half of what
anonymous
  • anonymous
but what about the other half? the teaspoon of honey? that is what i am really struggling with right now
anonymous
  • anonymous
The slope is the answer. 576 is the wrong answer. :)
anonymous
  • anonymous
so:
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anonymous
  • anonymous
yes, just remove the question mark otherwise the system will mark that as incorrect now, do you know how to find the slope from 2 given points? :)
anonymous
  • anonymous
\(\sf\Large Slope = \frac{\color{blue}{y_2}-\color{red}{y_1}}{\color{green}{x_2}-\color{purple}{x_1}}\) Where the two points are in the form: \(\sf\Large (\color{purple}{x_1},\color{red}{y_1})~and~(\color{green}{x_2},\color{blue}{y_2})\)
anonymous
  • anonymous
yes and that would be 16 which u say is the answer.
anonymous
  • anonymous
ok, now we need to find the slope from the table the slope which we get from the points in the table tells us the second half of the answer
anonymous
  • anonymous
so a teaspoons of honey and sugar are how many calories? i feel like we are getting no where
anonymous
  • anonymous
ok
anonymous
  • anonymous
since we are trying to find one teaspoon, the amount of calories of honey is 504, we just need to find the slope to that right?
anonymous
  • anonymous
Nope, we need to find the slope. The slope is the answer. You already found out that 1 teaspoon of sugar = 16 calories now we need to find out how many calories are equal to 1 teaspoon of honey
anonymous
  • anonymous
so one teaspoon of sugar is 16 calories? what is the amount for honey? that is what we are trying to find out
anonymous
  • anonymous
ok
anonymous
  • anonymous
that is what we are trying to find out, exactly!
anonymous
  • anonymous
how do we do that?
anonymous
  • anonymous
So can you tell me two points from the table? :)
anonymous
  • anonymous
any? ok two tablespoons is 568 calories, and 3 teaspoons is 696 calories
anonymous
  • anonymous
yes, any two points will work :)
anonymous
  • anonymous
so, you gave me these two points: (2,568) and (3,696)
anonymous
  • anonymous
\(\color{blue}{\text{Originally Posted by}}\) @TheЅmartOne \(\sf\Large Slope = \frac{\color{blue}{y_2}-\color{red}{y_1}}{\color{green}{x_2}-\color{purple}{x_1}}\) Where the two points are in the form: \(\sf\Large (\color{purple}{x_1},\color{red}{y_1})~and~(\color{green}{x_2},\color{blue}{y_2})\) \(\color{blue}{\text{End of Quote}}\) Now, you use this formula :)
anonymous
  • anonymous
ok i will tell you what i get one second, wait, what i get is the answer??
anonymous
  • anonymous
yes
whpalmer4
  • whpalmer4
Those are not all correct data...2 tsp is 568, 3 tsp is not 696...look at the table headings carefully!
anonymous
  • anonymous
I should have checked the points, mhmm. Whpalmer is correct.
anonymous
  • anonymous
so now what??
anonymous
  • anonymous
for the slope I got 1/128 btw
anonymous
  • anonymous
oops my bad let me do it again lol
anonymous
  • anonymous
ok :)
anonymous
  • anonymous
ok i got negative 1/128 is that it??
anonymous
  • anonymous
i need a whole number though
anonymous
  • anonymous
Remember, it's the change in y-values over the change in x-values
anonymous
  • anonymous
omg i know what i did wrong is it 64????
anonymous
  • anonymous
is this the final answer?????
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anonymous
  • anonymous
That is correct :)
anonymous
  • anonymous
yea!!!! thank u here is a medal and i will fan both of you!!!
anonymous
  • anonymous
i do need some more checking though do u mind helping me with that??
anonymous
  • anonymous
i will tag u in later bye for now!
anonymous
  • anonymous
Sure :)
whpalmer4
  • whpalmer4
That's the correct answer for this problem, but a teaspoon of honey has 21 calories, not 64 :-) A teaspoon of sugar does have 16 calories.
anonymous
  • anonymous
Haha, math problems never actually care about the factual stuff! I answered a problem a week ago that said a student had to walk to school. So he walked 4 miles north. And then 3 miles west. And it wanted to know the hypotenuse.
anonymous
  • anonymous
People were like: Who walks 7 miles to get to school?
whpalmer4
  • whpalmer4
Simple approach if you understand the meaning of the slope of a line here is to look at the honey table: \[ \begin{array}{cc} tsp & cal\\ 1 & 504 \\ 2 & 568 \\ 4 & 696 \\ 7 & 888 \\ \end{array} \] Pick two values where the independent variable (number of tsp of honey) changes by 1, and take the difference. That is your slope and calorie content of 1 tsp of honey. Going from 1 tsp to 2 tsp we go from 504 to 568, so adding 1 tsp adds \(568-504 = 64\) calories. Done.
whpalmer4
  • whpalmer4
If you don't have convenient adjacent values like that, then you have to divide by the number of teaspoons added to get the "unit rate" as it were.
TheSmartOne
  • TheSmartOne
Thanks for your great reply, as always! :)

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