Slopes: find slope of line thru (1997, 1.26), (2006, 2.31)

[kmomma1999]

Examine the rise in gasoline prices from 1997 to 2006. The price of regular unleaded gasoline in January 1997 was $1.26 and in January 2006 the price of regular unleaded gasoline was $2.31 (Bureau of Labor Statistics, 2006). Use the coordinates (1997, 1.26) and (2006, 2.31) to find the slope (or rate of change) between the two points. Describe how you arrived at your answer.

THis problem has been causing my headaches for two days. I know that the slope is the change in y and x. But after working through it two or three hundred times it seems to still evade me. I really would like to just know the steps to solving this. Maybe wsith other numbers, so that I may work this one out on my own. I want to make sure I know exactly how I get the answer so that I may do so on my exam next week. Thank you so much!!

 

[mmm4444bot]

Why not show us your work, so far?

... I know that the slope is the change in y and x ... ? Wrongly described

I really would like to just know the steps to solving this. ? Put your numbers into the slope formula and do the arithmetic

Hello KMomma:

In the future, please post your work. That's the best way for people to see what you've been doing with this exercise for 2 days.

You wrote that the slope is two numbers: the change in y and the change in x. This is not correct.

The slope of a line connecting two points is a single number. It is the change in y divided by the change in x.

Has anyone shown you the formula for slope?

If so, then have you ever used it?

\(\displaystyle \mbox{Slope} \;=\; \frac{Y2 - Y1}{X2 - X1}\)

There are only three steps.

1) Pick one of the xy-coordinates to be X1 and Y1 (it does not matter which one you choose)

2) Substitute your values for Y2, Y1, X2, and X1 into the slope formula

3) Do the arithmetic

EG: The coordinates for two points on a line are (4, 5) and (-3, -7). What is the slope of this line?

1) I pick (4, 5) to be (X1, Y1). Therefore,

Y2 = -7

Y1 = 5

X2 = -3

X1 = 4

2) I substitute these numbers into the slope formula.

\(\displaystyle \mbox{Slope} \;=\; \frac{-7 - 5}{-3 - 4}\)

3) I do the arithmetic.

-12/-7

The slope is 12/7

My experience with students who make mistakes calculating slope is that they are sloppy when substituting the numbers into the formula. They either mix up X1 with X2 OR they mix up Y1 with Y2.

Take care when substituting the coordinates into the slope formula.

If you need more help, then please share your work with us and explain WHY you're stuck.

Cheers,

~ Mark

 

[Deleted member 4993]

Re: Slopes

Examine the rise in gasoline prices from 1997 to 2006. The price of regular unleaded gasoline in January 1997 was $1.26 and in January 2006 the price of regular unleaded gasoline was $2.31 (Bureau of Labor Statistics, 2006). Use the coordinates (1997, 1.26) and (2006, 2.31) to find the slope (or rate of change) between the two points. Describe how you arrived at your answer.

THis problem has been causing my headaches for two days. I know that the slope is the change in y and x. But after working through it two or three hundred times it seems to still evade me. I really would like to just know the steps to solving this. Maybe wsith other numbers, so that I may work this one out on my own. I want to make sure I know exactly how I get the answer so that I may do so on my exam next week. Thank you so much!!

Do you see that the problem defines the co-ordinates (year, price) of two points in a graph?

If you are given two points (x[sub:d3y09r3q]1[/sub:d3y09r3q],y[sub:d3y09r3q]1[/sub:d3y09r3q]) & (x[sub:d3y09r3q]2[/sub:d3y09r3q],y[sub:d3y09r3q]2[/sub:d3y09r3q]) - the slope 'm' between those two points is

\(\displaystyle m \, = \, \frac{y_2 \, - \, y_1}{x_2 \, - \, x_1}\)

Find the relevant co-ordinates and find 'm'.

 

[Loren]

Re: Slopes

Suppose the data were 1920 the cost of sugar was $.19 a pound and in 1930 its cost was $.23 per pound.
If you let the x axes represent years and y axis represent cents (maybe you would want dollars), then you would have one point at (1920,19) and another at (1930,23)
Using the formula for slope we would have \(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{23-19}{1930-1920}=\frac{4}{10}=\frac{2}{5}\).

 

[kmomma1999]

Re: Slopes

OK I am new at this if you couldn't tell so I am sorry if I did not post what I needed to!! I understand the formula for the slope, but the part that I get stuck on is where each number goes into the formula.
The next thing I am unsure of is basically my math. Sometimes when I can get the numbers into the right places of the equation, I still get an answer that is wrong. I am not sure how to post my work so far, that is why I did not do it earlier. Again thank you and I am sorry that I am so new at this!!

 

[mmm4444bot]

Re: Slopes

I understand the formula for the slope, but the part that I get stuck on is where each number goes into the formula.

If you do not know how to make the substitutions, then you do NOT understand the formula.

The next thing I am unsure of is basically my math.

You have a calculator; if you are unsure of your arithmetic, then double-check your work.

I can get the numbers into the right places of the equation, I still get an answer that is wrong.

You just contradicted yourself. (Also, how do you know that your result is wrong?)

I am not sure how to post my work so far, that is why I did not do it

Please. You're going to have to do better than this.

You have the ability to type the following, correct? m = (1+2)/(3+4)

We need to see what you are doing!

Pick one of the xy-coordinates to be X1 and Y1.

Now, tell us the following.

Y2 = ?

Y1 = ?

X2 = ?

X1 = ?

After you answer these four questions, I will continue from there.

~ Mark

 

[kmomma1999]

Re: Slopes

You know I am sorry that I do NOT know what I am tyoping to get some help. I guess if I did understand it I would not be on this site asking for help and I would be finishing my assignment. I do not know how to type the equations into this box right here. I can type m+(1+2)/(3+4) but I was reffereing to the equation that was written about y1-y2 with x1-x2 under it. That is what I do not know how to type. I am sorry if I am really jumbled when I type, and sometimes I am not clear when I try to explain myself. Please understand that I have only been using a computer since I started college last November and what I do know about computers is self taught over the last ten months. Her is what I have so far.

2006-1997 9
----------- = ---
2.31-1.26 1.05
After this I am lost. I am not understanding how to eliminate the decimal point and make this into a fraction. I think that I can simplify this into 1
-------
5
but if I simplify it like that then how did I eliminate the decimal in the 1.05.

 

[mmm4444bot]

RE: Inability to type slope formula ...

... I can type m+(1+2)/(3+4) but I was reffereing to the equation that was written about y1-y2 with x1-x2 under it ... I am not understanding how to eliminate the decimal point and make this into a fraction.

m = (2006-1997)/(2.31-1.26) = 9/1.05 ? 8.57

If you want a ratio of two integers, then follow these steps.

\(\displaystyle \frac{9}{1.05} \;=\; \frac{9}{\frac{105}{100}} \;=\; 9 \cdot \frac{100}{105} = 9 \cdot \frac{20}{21} \;=\; \frac{60}{7}\)

Cheers,

~ Mark

 

[kmomma1999]

Re: Slopes

Thank you! That was exactly what I needed. Now I just hope that I can remember that concept throughout the rest of my classes. I only have one more math class after this one so I may be looking for help again in the coming weeks. Again thanks and have a good day!