Given the points ( 1 , 6 ) and ( 9 , 3 )
The slope of the line = m
[tex]m=\frac{rise}{run}=\frac{3-6}{9-1}=\frac{-3}{8}[/tex]so, the equation will be :
[tex]y=-\frac{3}{8}x+b[/tex]where b is a constant, we will find the value of b using the point ( 1 , 6 )
when x = 1 , y = 6
so,
[tex]\begin{gathered} 6=-\frac{3}{8}\cdot1+b \\ b=6+\frac{3}{8}=\frac{51}{8} \end{gathered}[/tex]so, the equation of the line is:
[tex]y=-\frac{3}{8}x+\frac{51}{8}[/tex]The standard form of the line will be as following:
Multiply the equation by 8
So,
[tex]\begin{gathered} 8y=-3x+51 \\ \\ 3x+8y=51 \end{gathered}[/tex]