Question

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

Answer 1

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:
`slope=(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:

`(x,y)` and `(4/5,0)`

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+(4/5)`