Question

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?

Answer 1

i think the tablespoon of sugar is 576, but what is the tablespoon of honey plz help?

Answer 2

@dan815 @sleepyjess @just_one_last_goodbye @SolomonZelman @KendrickLamar2014

Answer 3

i meant teaspoon not tablespoon my bad

Answer 4

Hi there!

Answer 5

hi may you plz help?

Answer 6

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.

Answer 7

\[ y = 16x + 560\]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).

Answer 8

ok

Answer 9

@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.

Answer 10

for the teaspoon of sugar i got 576, was that correct? if not, i will need some extra help

Answer 11

576 calories i mean

Answer 12

@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.

Answer 13

@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?

Answer 14

@TheSmartOne the slope is 16

Answer 15

now what?

Answer 16

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.

Answer 17

which is 576 correct? so i am right for half of what

Answer 18

but what about the other half? the teaspoon of honey? that is what i am really struggling with right now

Answer 19

The slope is the answer.

576 is the wrong answer. :)

Answer 20

so:

Answer 21

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? :)

Answer 22

\(\sf\Large Slope = \frac{\color{blue}{y_2}-\color{red}{y_1}}{\color{green}{x_2}-\color{purple}{x_1}}\)

Where the two points are in the form:

\(\sf\Large (\color{purple}{x_1},\color{red}{y_1})~and~(\color{green}{x_2},\color{blue}{y_2})\)

Answer 23

yes and that would be 16 which u say is the answer.

Answer 24

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

Answer 25

so a teaspoons of honey and sugar are how many calories? i feel like we are getting no where

Answer 26

ok

Answer 27

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?

Answer 28

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

Answer 29

so one teaspoon of sugar is 16 calories? what is the amount for honey? that is what we are trying to find out

Answer 30

ok

Answer 31

that is what we are trying to find out, exactly!

Answer 32

how do we do that?

Answer 33

So can you tell me two points from the table? :)

Answer 34

any? ok two tablespoons is 568 calories, and 3 teaspoons is 696 calories

Answer 35

yes, any two points will work :)

Answer 36

so, you gave me these two points:

(2,568) and (3,696)

Answer 37

\(\color{blue}{\text{Originally Posted by}}\) @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 :)

Answer 38

ok i will tell you what i get one second, wait, what i get is the answer??

Answer 39

yes

Answer 40

Those are not all correct data...2 tsp is 568, 3 tsp is not 696...look at the table headings carefully!

Answer 41

I should have checked the points, mhmm.

Whpalmer is correct.

Answer 42

so now what??

Answer 43

for the slope I got 1/128
btw

Answer 44

oops my bad let me do it again lol

Answer 45

ok :)

Answer 46

ok i got negative 1/128 is that it??

Answer 47

i need a whole number though

Answer 48

Remember, it's the change in y-values over the change in x-values

Answer 49

omg i know what i did wrong is it 64????

Answer 50

is this the final answer?????

Answer 51

That is correct :)

Answer 52

yea!!!! thank u here is a medal and i will fan both of you!!!

Answer 53

i do need some more checking though do u mind helping me with that??

Answer 54

i will tag u in later bye for now!

Answer 55

Sure :)

Answer 56

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.

Answer 57

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.

Answer 58

People were like: Who walks 7 miles to get to school?

Answer 59

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.

Answer 60

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.

Answer 61

Thanks for your great reply, as always! :)