linear function for occupants in terms of rental fees

[heathurr07]

So on my math quiz there was a problem that I couldn't seem to solve right:

If an owner of an apartment complex charges $700 rent, he has 80 occupants. If he charges $800, he has 60. Make a linear function that shows this relationship, graph it, and find how many occupants he will have if he charges $760.

For some reason, I kept coming up with a negative number for the last part.
The equation I got was y=(-5)x+3850


What did I do wrong, and what is the answer?


It's driving me nuts!

 

[galactus]

Re: linear function.. help please.

You have the wrong line equation. Perhaps you worked it backwards. y/x, not x/y.

Use your info to find the line equation and then just plug in x=760.

You have (700,80) and (800,60)

Slope is \(\displaystyle m=\frac{60-80}{800-700}=\frac{-1}{5}\)

Now use y=mx+b. Use either of your points for x and y and then solve for b. There's your line equation.

Now, plug in x=760.

 

[heathurr07]

Re: linear function.. help please.

I tried that as well, but then I came up with a negative number of occupants for $760. (-52 occupants)

Am I missing something? Hah.

 

[galactus]

Re: linear function.. help please.

You can not have negative occupants. The line equation is \(\displaystyle y=\frac{-x}{5}+220\)

 

[heathurr07]

Okay, I see what I did wrong now. For some reason my mind decided to think that -800/5 was -40. Don't ask me why. Haha, thanks for your help!