y = - \frac{2}{5} x - 2
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 2x + 5y = 10 into this form
subtract 2x from both sides
5y = - 2x + 10 ( divide all terms by 5 )
y = - \frac{2}{5} x + 2 ← point- slope form with slope m = - \frac{2}{5}
Parallel lines have equal slopes hence
y = - \frac{2}{5} x + c is the partial equation of the parallel line
to find c, substitute ( 5, - 4 ) into the partial equation
- 4 = - 2 + c ⇒ c = - 4 + 2 = - 2
y = - \frac{2}{5} x - 2 ← equation of parallel line
