Answer:
4x - 5y + 30 = 0
Step-by-step explanation:
When a slope of a line and a point passing through it is given then we use slope - one point form to determine the equation of the line.
It is given by:
[tex]$ (y - y_1) = m (x - x_1) $[/tex]
where [tex]$m$[/tex] is the slope of the line and
[tex]$ (x_1, y_1) $[/tex] is the point passing through it.
Here [tex]$m = \frac{4}{5} $[/tex] and [tex]$ (x_1 , y_1) = (-5,2) $[/tex].
Substituting in the equation we get
[tex]$ (y - 2) = \frac{4}{5} (x + 5) $[/tex]
[tex]$ \implies 5y - 10 = 4x + 20 $[/tex]
[tex]$ \implies 4x - 5y + 30 = 0 $[/tex]
