Punktsteigungsform. Verstehe Lösungsweg nicht.

Question

kann mir jemand bitte dabei helfen?

1.    I=0.5(18+m)

A landlord determines that the total amount of income, I, in thousands of dollars generated by renting out a home is given by the equation above. Negative values of m represent the time m months before January 1,2010 and positive values of m represent the time m months after January 1,2010. The landlord had a income of 0 when thw home was bought and only began receiving income from rent afterward. When did the landlord buy the home?

Lösung: Because the income is 0 when the landlord bought tje home, we are looking for the root of the linear equation. The root is written in the form:

I=a(m-m0)

In this equation, a is a constant and m0 is the root. Because addition is the same as subsätracting a negative, we can rewrite the original equation as:

I=0,5(m-(-18))

We see that -18 corresponds to the rooot of the equation, so the income is 0 when m is -18. Therefore, the home was bought 18 months before January 1,2010.

Comments

Okay verstanden. War glaube ich etwas zu müde :D

Answer 1

> Negative values of m represent the time m months before January 1,2010

Let m be -10.

Then m is negative.

Therefore -10 represent the time -10 months before January 1,2010

-10 months before January 1,2010 is 10 month after January 1,2010, i.e. October 1, 2010.

> and positive values of m represent the time m months after January 1,2010.

Now let m be 10.

Then m is positive.

Therefore 10 represent the time 10 months after January 1,2010.

10 months after January 1,2010 is (as I mentioned before) October 1, 2010.

> The landlord had a income of 0 when thw home was bought

Now let's see for which value of m is I = 0:

0=0.5(18+m) ⇔ 0 = 18+m ⇔ -18 = m.

Because m is negative it represents 18 month after January 1,2010, i.e. July 1, 2011.