Calculus

I asked for help on a question yesterday and I got really good help and I was wondering if someone could help with this problem too.

This is the question:
Find an equation of the line through the point (1,3) that cuts off the least area from the first quadrant.

My work on the problem so far:
I know that it will be in the first quadrant and that the result will form a right triangle.
I have written the equation y=-mx+b because I do know that the line will be decreasing.
Besides that, I do not know what to do.
Can someone help me please?

If you take the equation for the line to be:

y=-mx+b (1)

then you have to require that if x = 1, y = 3. So, you insert these figures in Eq. (1) and you get:

3 = -m + b (2)

This equation does not fix m and b but relates the two. This is what you would expect, because you can draw a line through the point (1,3) in an infinite number of ways. You then calculate where the line will intersect the x-axis. At that point y=0, so:

-mx + b =0 -->

x = b/m

And the line intersects the Y-axis when x = 0, so the y-coordinate at that point is b.

This maens that the right traingle as its three corners at:

(0,0), (0,b) and (b/m,0)

The area of the triangle is thus:

A = 1/2 b^2/m (3)

If you use Eq. (2) to express b in terms of m:

b = 3 + m and insert that in (3), you find:

A = 1/2 (3 + m)^2/m =

1/2 (9/m + 6 + m)

If you equate the derivative of this to zero you find:

m = 3.

  1. 👍 0
  2. 👎 0
  3. 👁 152

Respond to this Question

First Name

Your Response

Similar Questions

  1. history

    a question i asked yesterday why was the assyrian empire considered the first? i don't have enough specifics can i have some help

    asked by qwerty on September 14, 2008
  2. SAT Math... again

    I asked two questions yesterday, and thankfully, bobpursley answered the latter. I accidentally typed in the first question wrong, so I'd really appreciate it if someone helps me out. Thank you, and have a good day :) 1. Kevin is

    asked by Lacey on October 15, 2007
  3. English

    hi im sam :p i have 8th grade math and i think like yesterday we got an assesment called circle sentencing and im completly confused i even asked my princble and she couldn't even help..:( i have a link to show what my homework is

    asked by samm on September 8, 2011
  4. Geography (Ms.Sue)

    Yesterday I asked this question- 29. One of Eastern Europe's most valuablee natural resouces, sometimes called its "lifeline" is the a. Volga river b. Danube river c. Rhine river d. Oder river I asked my teacher because I was

    asked by mysterychicken on October 1, 2009
  5. Science-Help Please

    What is a concept map. I've asked that same question yesterday as well, but I don't think anyone noticed. Can someone please tell me how to create one for the milky way,thanks in advance.

    asked by Sara on March 2, 2010
  6. Jennifer

    I asked this question yesterday and it was answered, but I still have a question on it. Standard entropies for substances are defined at a pressure of exactly 1 bar in some books or exactly 1 atm(760 torr) in different books. For

    asked by Chemistry on April 4, 2007
  7. English

    Hey, Yesterday I asked a question about "the" and Writeacher helped me a lot. But now I have a further question. I have a rule in my grammar book, which says, that Nationalities with the suffix -ese. -ch, -sh, -ss; goes with the.

    asked by Minnie on December 17, 2012
  8. Math

    I asked this question yesterday, but I am still having alot of trouble, can someone please help me. Thanks. If 1-cos^2x=0.8725, and x is acute, determine the value of x correct to the nearest tenth of a degree.

    asked by Sydney on April 19, 2009
  9. English

    Thank you very much! Just one more thing. Should I evaluate the following sentence a mistake? 1) The journalist asked where I was going to sing ...... (istead of "asked me") The officer asked if I could show him my permit (instead

    asked by Henry on March 5, 2012
  10. Grammar

    While they watched the movie, the kids clapped cheered and ate popcorn. RULE(S):_______________________________________________ Jack and Jill watched a bunch of different soccer games but Riccardo’s favorite was the Valencia

    asked by Anonymous on January 12, 2020
  11. Social studies

    What is the importance of History? I was asked this and was like, umm to learn about important old things. *face palm* opps not how I wanted it to come out. (I got nervous) now my teacher asked my to write a paragraph answering

    asked by Help? on September 28, 2016

More Similar Questions