For this case we have that by definition, the point-slope equation is given by:
[tex](y-y_ {0}) = m (x-x_ {0})[/tex]
Where:
m: It's the slope[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}\\(x_ {1}, y_ {1}) :( 0,0)\\(x_ {2}, y_ {2}): (- 5,4)[/tex]
Substituting:
[tex]m = \frac {4-0} {- 5-0} = - \frac {4} {5}[/tex]
Thus, the equation is of the form:
[tex](y-y_ {0}) = - \frac {4} {5} (x-x_ {0})[/tex]
We substitute a point:[tex](y-0) = - \frac {4} {5} (x-0)\\y = - \frac {4} {5} x[/tex]
Answer:
[tex]y = - \frac {4} {5} x[/tex]
