Hello Duffmac

Welcome to Math Help Forum! Originally Posted by

**Duffmac** Hi for class i have a hundred problem assignment and out of all the problems a few have stumped me i know there not difficult but i am having trouble, i just want to do really good on this assignment , if you can help thanks.

1.)The business opened with a debt of $4300. After 2 years, it accumulated profit of $4600. Find the profit as a function of time

, knowing the profit function is linear.

I'm not exactly sure what the question means by the word 'accumulated'. Does it mean (a) that in two years it *made *a profit of $4600, and so was now $300 in surplus? Or does it mean (b) that in two years it made enough profit to wipe out the debt and is now $4600 in surplus? (It would need to have made $8900 profit to do this.) Here are both answers.

(a) If the function is linear, then it means that the profit each year is constant. So that's $\displaystyle 4600\div2 = 2300$ per year. After t years, then, the profit will be $\displaystyle P(t)=2300t$.

(b) In a similar way, this time $\displaystyle P(t) = -4300 + 4450t$.

2.)) Find the slope and the y-intercept of the line

$\displaystyle y = 10(9x-9)$$\displaystyle =90x -90$

This is now in the form $\displaystyle y = mx +c$, so the slope is $\displaystyle 90$, and the intercept is $\displaystyle -90$.

3.)The equation of the line with slope

that goes through the point

can be written in the form

where

is

The value of $\displaystyle m$ is $\displaystyle -1$ (the slope). If you want the value of $\displaystyle b$ as well, plug in the values of $\displaystyle x$ and $\displaystyle y$ that you know (and this value of $\displaystyle m$), to get:

$\displaystyle -2=(-1)(5)+b$

Can you solve this equation now to find $\displaystyle b$?

4.)Find the

- and

-intercepts of the graph of the equation

The $\displaystyle y$-intercept is where $\displaystyle x$ has the value $\displaystyle 0$. So that's $\displaystyle y =-40$.

For the $\displaystyle x$-intercepts (there are two), give $\displaystyle y$ the value $\displaystyle 0$:

$\displaystyle x^2+3x-40=0$

$\displaystyle \Rightarrow (x+8)(x-5)=0$

Can you complete this quadratic equation?

Grandad