Answer :
The equation of a line in standard form looks like this...
[tex]aX+bY=c[/tex]Points
(x1,y1) = (3 , -14)
(x2,y2) = (2 , 5)
[tex]\text{if y=mx+b; then m is the slope m=(y2-y1)/(x2-x1)}[/tex][tex]m=\frac{5-(-14)}{2-3}=-\frac{19}{1}=-19[/tex][tex]y=-19x+b[/tex]if we substitute for the first point:
[tex]\begin{gathered} -14=-19\cdot(3)+b \\ -14=-57+b \\ b=57-14=43 \end{gathered}[/tex]Therefore,
[tex]y=-19\cdot x+43[/tex]Now, we want to write this equation in standard form:
[tex]\begin{gathered} y=-19x+43 \\ +19x+y=+19x-19x+43 \\ 19x+y=43 \end{gathered}[/tex]Therefore a=19 ; b=1 and c=43
