Superman needs to save Lois from the clutches of Lex Luthor. After flying for 6 seconds, he is 1900 meters from her. Then at 13 seconds he is 1550 meters from her.

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- mathmale

JANB: Are you sure that this is all the info supplied? I don't see any question here!

- anonymous

Write an equation to model this situation (use m for meters and s for seconds).

- mathmale

You are given 2 sets of info: (6 seconds, 1900 meters) and (13 seconds, 1550 meters). You may as well assume that this guy flies in a straight line (even though i don't).
So you are given two points; you need to imagine that our hero flies from one point to the next.
You need to come up with a mathematical model that describes his inflight adventure. How do you describe a straight line?

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- anonymous

Its 180 degrees? I am honestly really lost with this question.

- mathmale

if you were to fly from Los Angeles to New York, your flight path would have "slope," since NY is north of, as well as to the east of, LA. How would you find that slope?
Let me estimate that NY is 800 miles north of LA and 3000 miles east of LA. What is the slope of that flight line?

- anonymous

That's extremely confusing to be honest.
y=800x+3000?
no? I don't know?

- anonymous

Calculate the slope first.\[\frac{ 1900 -1550 }{ 13-6 }=50\]This means Superman is flying at a rate of 50 m/s. Then you use the point-slope formula by picking one of the two points.\[y-1550=50(x-6)\] I'll leave it to you to convert this in slope-intercept form.

- anonymous

I got 50 but I was not sure what to do next.
I should've known to use the y-y1=m(x-x1)
I'm such an idiot !

- mathmale

In fairness, I should present (or review) the concept of slope.
It helps to think of "slope" as rise over run.
To get to NY from LA, you'd have to fly 800 miles north and at the same time 3000 miles east. The "rise" (motion in the vertical direction) is 800 miles; the "run" (motion in the horizontal direction) is 3000 miles. Therefore, the slope, m, is \[m=\frac{ rise }{ run }=\frac{ 800 miles }{ 3000 miles }=\frac{ 8 }{ 30 }=\frac{ 4 }{ 15 }.\]

- mathmale

Have you seen this formula before?

- anonymous

Yeah I have, I just am not really sure when to use what formula if that makes any sense.

- mathmale

In the math problem you want to solve: your initial point is (6,1900); your final point is (13,1550). Here the 6 and 13 represent TIME and are on the horizontal axis; the 1900 and the 1550 represent how far SuperGuy is from Lois.
The "run" is the difference between 6 and 13: 13-6=7.
The "rise" is the difference between 1900 and 1550: 1550-1900=350./
thus, the slope is m = rise/run, or 7/(-350), or -7/350.

- mathmale

I must apologize: I have the order wrong in my statement, "the slope is -7/350." I should have typed, the slope is -350 meters / 7 seconds, or -50 meters/second. sorry.

- triciaal

negative distance with positive time the slope should be negative
as he gets closer the time is increasing

- mathmale

How are you doing? Does this make sense, or do you need clarification?

- mathmale

tricia: Agreed. The slope is -50 meters/ sec.

- mathmale

As Tricia says, SuperGuy's distance from the hapless Lois decreases with time, at the rate of 50 meters/sec.

- mathmale

Jean: Awaiting a response from you.

- anonymous

I used the information you gave me and came up with this y-1550=-50(x-13) ?

- anonymous

Am I using it wrong ?

- triciaal

the objective i think is to find x when y = 0
how long will it take to rescue Lois
to get from

- triciaal

you have 2 unknowns in what you have written

- triciaal

this is what I would normally do
after finding the slope use one of the given points to find the intercept
using the equation of the line find other points on the line
slope = -50
using (6, 1900)
1900 = -50(6) + b
1900 + 300 = b = 2200
y = -50(x) + 2200

- triciaal

the question asked only for the equation

- mathmale

I agree: "Write an equation to model this situation (use m for meters and s for seconds)."

- anonymous

I have been on this problem for hours trying to figure out what I needed to do.
But I think I get it now. You plugged in what you found into the slope intercept form, that makes much more sense.

- triciaal

distance traveled in meters,m = 50s + 2200

- mathmale

Tricia, wouldn't the independent variable be time (t)? Yes, we're measuring time in seconds (s), but nevertheless the equation should be
d = distance = [(-50 meters)/sec]t + 2200 meters.

- triciaal

from the information given , the 2 points, find the slope of the line
we have points and the slope we can find the equation of the line

- mathmale

I'm not arguing with your result: distance traveled in meters,m = 50s + 2200
But I am stating that units of measurement are required, and that your equation would be better if written as
\[d=(\frac{ -50 meters }{ \sec })t + 2200 meters,\]
where t is, of course, measured in seconds (s).

- anonymous

Thank you, both of you by the way !

- triciaal

@mathmale yes that would be more precise.
@jeaannebad your welcome

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