|
Question 160269: I have a word problem that deals with rate of change. The word problem reads as follows: In 1927, Charles Lindbergh made history by making the first translantic flight from New York to Paris. It took Lindbergh approximately 33.5 hours to make the trip. In 1997, the Concorde could make the trip in approximately 3.3 hours. This data can be written in table format, where the input represents the year and the output represents the number of hours between two cities.
The two sets of coordinates are: (33.5, 1927) (3.3, 1997).
My slope = -3.02/7 Which I interpret as The number of hours have decreased between the transatlantic flight from New York to Paris at a rate of -3.02 hours per 7 years.
The point intercept slope is y = -3.02x/7 + 6054.04/7 or y = -3.02x/7 + 864.9. Here is where my confusion is why do I end up with a y-intercept as 864.9 such a hugh number. As a result, when I graphed the two points above my y-intercept is 38 hours, that is, If I labled my graph correctly. on the y-axis I started with 0 - 80 starting with 10 and increasing the number by increments of 10. My x-axis I started with year '27 again with increaments of 10 up to the year '07.
Can you help me out. I am so lost with the point intercept linear equation. Help! am I doing something rong.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! i think your problem is you started with an x value that is way out there (1927).
you are so far from the y intercept and the slope is so steep going down from left to right (or going up from right to left), that the y intercept will be very large because when x = 0, this represents the year 0.
-----
if you pose the problem differently, then the y intercept will be the value of y in the year 1927.
-----
you do that by making x = the year - 1927.
then for 1927, the value of x is 0, and for 1997, the value for x is 70.
then your graph will look much better.
-----
now you have
x1 = 0, y1 = 33.5
x2 = 70, y2 = 3.3
your slope was correct and is (-3.02/7)
equation for slope intercept form of the equation of the line is 
this becomes y = (-3.02/7)*x - (-3.02/7)*0 + 33.5
this becomes y = (-3.02/7)*x + (3.02/7)*0 + 33.5
this becomes y = (-3.02/7)*x + 33.5
your y-intercept is 33.5 as it should be since this is when x equals 0 and when x = 0, the year is 1927.
-----
in your original equation, x1 was 1927 and y1 was 33.5
slope was the same (-3.02/7)
slope intercept form of the equation should have been y = (-3.02/7)*(x - 1927) + 33.5 which becomes
y = (-3.02/7)*x - (-3.02/7)*1927 + 33.5
which becomes
y = (-3.02/7)*x + (3.02/7)*1927 + 33.5
which becomes
y = (-3.02/7)*x + 831.26285... + 33.5
which becomes
y = (-3.02/7)*x + 864.8628...
which becomes 864.9
-----
everything you did was correct, and if you let the x values remain as you originally made them, the y-intercept should be 864.9 because that is the year 0.
|
|
|
| |
