# Thread: how find the formula

1. ## how find the formula

I'm really stuck on this question, I have tried it and read through my notes but can't find a way to solve it. Help would be greatly appreciated.

A linear function f(x) passes through a point (-2,3) and agrees with the condition f(x)dx = -44. What is the formula?

ps: sorry for the paint drawing. I didnt know how else to show it.

2. Originally Posted by JQ2009
I'm really stuck on this question, I have tried it and read through my notes but can't find a way to solve it. Help would be greatly appreciated.

A linear function f(x) passes through a point (-2,3) and agrees with the condition f(x)dx = -44. What is the formula?

ps: sorry for the paint drawing. I didnt know how else to show it.
$\displaystyle y = mx+b$

point $\displaystyle (-2,3)$ is on the line ...

$\displaystyle 3 = -2m+b$

$\displaystyle b = 2m+3$

$\displaystyle \int_2^4 mx+b \, dx = -44$

$\displaystyle \int_2^4 mx + (2m+3) \, dx = -44$

evaluate the definite integral, solve for $\displaystyle m$ ... calculate $\displaystyle b$.