Find the equation, in standard form of the line passing through the points (3,-4) and (5,1)

Find the slope
slope bewteen points (x1,y1) and (x2,y2) is
(y2-y1)/(x2-x1)
given
(3,-4) and (5,1)
slope=(1-(-4))/(5-3)=(1+4)/2=5/2

in form
y-y1=m(x-x1)
slope is m an a point on the line is (x1,y1)
so
a point is (5,1)
slope is 5/2
y-1=5/2(x-5)
expand
y-1=5/2x-25/2
y=5/2x-23/2

standard form is ax+by=c where a is normally positive and a,b,c are whole numbers
so multiply everybody by 2
2y=5x-23
minus 5x both sides
-5x+2y=-23
times -1 both sides
5x-2y=23

the equation is 5x-2y=23

The linear equation is: y=ax+b