Interpret the Slope

[mathdad]

The following data represent the weight (in grams) of a box of raisins and the number of raisins in the box.

Weight (in grams) w

42.3
42.3
42.8
42.4
42.6

Number of Raisins R

87
87
93
87
89

Note: The variables w and R represent a point in the form ( w, R).

Use the data above to interpret the slope m.

Question:

What exactly is the question asking? Is the question asking to find the slope m?

 

[Deleted member 4993]

The following data represent the weight (in grams) of a box of raisins and the number of raisins in the box.

Weight (in grams) w

42.3
42.3
42.8
42.4
42.6

Number of Raisins R

87
87
93
87
89

Note: The variables w and R represent a point in the form ( w, R).

Use the data above to interpret the slope m.

Question:

What exactly is the question asking? Is the question asking to find the slope m?

I think they are asking about the slope of best-fit-line through those points.

What have you been taught about best-fit-line?

 

[Harry_the_cat]

You can find a value for m by finding the slope of the line of best fit. Refer to your other post.

I think this question is asking you to interpret the meaning of that value.

Let's just say the slope works out to be 6 (you'll need to work it out properly). What does that 6 mean?

Recall that slope =\(\displaystyle \frac{\Delta y}{\Delta x}\) or in this case \(\displaystyle \frac{\Delta R}{\Delta w}\).

So, does the slope of 6 mean "6 raisins per gram" or "6 grams per raisin"?

 

[mathdad]

Khan:

1. I am not a student. I am simply reviewing college algebra.
2. I did not see anything in the textbook chapter Linear Models: Building Linear Functions From Data about BEST-FIT-LINES.

 

[mathdad]

You can find a value for m by finding the slope of the line of best fit. Refer to your other post.

I think this question is asking you to interpret the meaning of that value.

Let's just say the slope works out to be 6 (you'll need to work it out properly). What does that 6 mean?

Recall that slope =\(\displaystyle \frac{\Delta y}{\Delta x}\) or in this case \(\displaystyle \frac{\Delta R}{\Delta w}\).

So, does the slope of 6 mean "6 raisins per gram" or "6 grams per raisin"?

Let m = 6.

If the weight of a candy is increased by one gram, the number of calories will increase by the value of m or 6, on average. Is this ok for an answer?

 

[Dr.Peterson]

Let m = 6.

If the weight of a candy is increased by one gram, the number of calories will increase by the value of m or 6, on average. Is this ok for an answer?

Are you answering a different question? The question in this thread is about raisins and grams, not about candy grams and calories.

 

[mathdad]

Are you answering a different question? The question in this thread is about raisins and grams, not about candy grams and calories.

Yes, I made a mistake and posted an answer to a different question from the same chapter.

The question asked here:

So, does the slope of 6 mean "6 raisins per gram" or "6 grams per raisin"?

I am not too clear about how to answer this question, if for example, the slope is 6.

 

[Harry_the_cat]

The slope isn't 6. You will need to calculate that for your line of best fit.

Whatever the figure is though needs to be interpreted, in other words, it must have units attached.

Let your calculation of slope guide you as to what units are involved.
Since the slope is calculated as \(\displaystyle \frac{\Delta y}{\Delta x}\) then the units will be y units per x units.

So, in this case, the slope is in raisins/gram.

 

[mathdad]

The slope isn't 6. You will need to calculate that for your line of best fit.

Whatever the figure is though needs to be interpreted, in other words, it must have units attached.

Let your calculation of slope guide you as to what units are involved.
Since the slope is calculated as \(\displaystyle \frac{\Delta y}{\Delta x}\) then the units will be y units per x units.

So, in this case, the slope is in raisins/gram.

Your replies are amazingly simple to read and understand. I hope to receive help from you for the rest of my college algebra review and beyond.