Question

Im trying to solve. Whats the ordered pairs are the line 3x-4y=9My choices are (1, 3/2)(-1,3)(-5,-6)(2/3, -7/4)Please help me solve thisThanks

Answer 1

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):

`\begin{gathered} 3x-4y=9 \\ 3(1)-4((3)/(2))=9 \\ 3-(12)/(2)=9 \\ 3-6=9 \\ -3=9\longrightarrow\text{False} \end{gathered}`

We now try with (-1,3):

`\begin{gathered} 3x-4y=9 \\ 3(-1)-4(3)=9 \\ -3-12=9 \\ -15=9\longrightarrow\text{False} \end{gathered}`

We now try with (-5,-6):

`\begin{gathered} 3(-5)-4(-6)=9 \\ -15+24=9 \\ 9=9\longrightarrow\text{True} \end{gathered}`

The point (-5,-6) belong to the line 3x - 4y = 9.

We can finally test (2/3, -7/4):

`\begin{gathered} 3((2)/(3))-4((-7)/(4))=9 \\ 2+7=9 \\ 9=9\longrightarrow\text{True} \end{gathered}`

Answer: The ordered pairs that belong to the line are (-5,-6) and (2/3, -7/4).