1. ## Linear Supply Functions?

I'm trying to find out the linear supply function and this is what I have so far, which may be all wrong.

(60, 40) and (100, 60)
M = 60 – 40/ 100 – 60 = 20/40
S (x) – 60 = 20/40 (x – 60)

Supply: For a new diet pill, 60 pills will be supplied at a price of $40, while 100 pills will be supplied at a price of$60. Write a linear supply function for this product.

2. You've got the right idea. You have the points:

(60, 40) and (100, 60). You want to find the slope, as you know, but you found the slope incorrectly. The slope is the difference in the y-coordinates divided by the difference in the x-coordinates:

$\displaystyle \frac{40-60}{60-100} = \frac{-20}{-40} = \frac {1}{2}$.

So now you know the slope, m. Use point-slope form (with either point) to write the equation. Point-slope form:

$\displaystyle (y - y_1) = m(x-x_1)$

where $\displaystyle (x_1,y_1)$ are the coordinates of EITHER of your two points, your choice.

3. Thanks so much for your help. I came up with this answer for the linear supply equation so hopefully this is right.
S (x) = 1
----x - 10
2

4. Thanks so much for your help. I came up with this answer for the linear supply equation so hopefully this is right.
S (x) =
1
----x - 10
2

5. Not quite what I got - I got $\displaystyle y = \frac{1}{2}x+10$, not -10.

$\displaystyle (y-40)= \frac{1}{2}(x-60)$

$\displaystyle y - 40 = \frac{1}{2}x - 30$

Add 40 to both sides gives:

$\displaystyle y = \frac{1}{2}x+10$.

Perhaps just a sign error, I suspect.