Write an equation in slope-intercept form and then in standard form for each line described. y-intercept -2; x-intercept 5

Hello
the line passes by A ( 0 ; -2)  and B (5 ; 0) equation : y = ax+b
a is a slop : a = (yb - ya)/(xb -xa)
a = (0+2)/(5-0)
a =2/5
y = (2/5)x+b
if x=5 and y= 0
0 = (2/5)(5)+b
b= - 2
the equation is : y = (2/5)x-2