# How do you write the equation of a line given the line has a slope of –1 and contains the point (4/5,0)?

Dec 17, 2014

This is a good question!
You have 2 clues:
the first one is the slope!
The slope tells you how y changes when x changes or:
$s l o p e = \frac{\Delta y}{\Delta x}$
where $\Delta y = {y}_{2} - {y}_{1}$ and $\Delta x = {x}_{2} - {x}_{1}$

The second clue are the values of ${x}_{2} , {y}_{2}$ and ${x}_{1} , {y}_{1}$ ! Only one is fixed the other can be chosen at will.
You can choose:

$\left(x , y\right)$ and $\left(\frac{4}{5} , 0\right)$

So substituting in the expression. for the slope you get:

-1=(y-0)/(x-(4/5)

Rearranging, the equation of the line becomes:

$y = - x + \left(\frac{4}{5}\right)$