Hi there can you help me find the equation of the line that has a slope of -4/3 and passes through (-2,5) ?
Thank you!
The formula for the equation of a line knowing 2 points and a slope is:
$\displaystyle y-y_1 = m(x-x_1)$ where m is the slope and $\displaystyle x1$ and $\displaystyle y1 $ are the coordinates of the given point.
Simply substitute:
$\displaystyle y-5 = -\frac{4}{3} (x- (-2))$ and clean up if you want. Usually, on AP Calc tests, they recommend you don't waste your time simplifying because they accept this answer.
$\displaystyle y=ax+b$
$\displaystyle a=m=\frac{-4}{3}$
$\displaystyle 5=\frac{-4}{3}(-2)+b
$
$\displaystyle 5=\frac{8}{3}+b$
$\displaystyle b=5-\frac{8}{3}$
$\displaystyle b=\frac{7}{3}$
$\displaystyle y=\frac{-4}{3}x+\frac{7}{3}$
Just as a different method