We have to find the points, as ordered pairs, that belong to the line 3x - 4y = 9.
For an ordered pair (x,y) to belong to a line, it has to satisfy the equation of the line.
We have to check for each one. We replace x and y with the values of the ordered pair and check the equation.
We start with (x,y) = (1,3/2):
[tex]\begin{gathered} 3x-4y=9 \\ 3(1)-4(\frac{3}{2})=9 \\ 3-\frac{12}{2}=9 \\ 3-6=9 \\ -3=9\longrightarrow\text{False} \end{gathered}[/tex]We now try with (-1,3):
[tex]\begin{gathered} 3x-4y=9 \\ 3(-1)-4(3)=9 \\ -3-12=9 \\ -15=9\longrightarrow\text{False} \end{gathered}[/tex]We now try with (-5,-6):
[tex]\begin{gathered} 3(-5)-4(-6)=9 \\ -15+24=9 \\ 9=9\longrightarrow\text{True} \end{gathered}[/tex]The point (-5,-6) belong to the line 3x - 4y = 9.
We can finally test (2/3, -7/4):
[tex]\begin{gathered} 3(\frac{2}{3})-4(\frac{-7}{4})=9 \\ 2+7=9 \\ 9=9\longrightarrow\text{True} \end{gathered}[/tex]Answer: The ordered pairs that belong to the line are (-5,-6) and (2/3, -7/4).
