Question

5.Here is a graph of the equation 3x - 2y = 12.Select all coordinate pairs that represent a solution to the equation.y2-2XS24246a.(2, -3)b.(4,0)C.(5.-1)d. (0,-6)

Answer 1

We are asked to determine which point are solutions to the equation:

`3x-2y=12`

since we are given a graph, a point is a solution to the equation if it is in the line.

For point (2, -3) we that this point is in the line therefore, it is a solution to the equation. we can prove this analytically by replacing the values of x and y in the equation:

`\begin{gathered} 3(2)-2(-3)=12 \\ 6+6=12 \\ 12=12 \end{gathered}`

For point (4,0) we see that it is on the line, therefore it is a solution. Replacing in the equation:

`\begin{gathered} 3(4)-2(0)=12 \\ 12=12 \end{gathered}`

For point (5, -1), we notice that it is not in the line, therefore, it is not a solution. Replacing in the equation:

`\begin{gathered} 3(5)-2(-1)=12 \\ 15+2=12 \\ 17\\e12 \end{gathered}`

For point (0, -6), we see that the point is in the graph, therefore, it is a solution. Replacing in the equation:

`\begin{gathered} 3(0)-2(-6)=12 \\ 12=12 \end{gathered}`