In order to graph the equation, we need to find two ordered pairs that are solutions to the equation.
To do so, we can choose values for x and then calculate the corresponding values of y.
So, for x = 2 and x = 4, we have:
[tex]\begin{gathered} x=2\colon \\ 6-2y=16 \\ 2y=-10 \\ y=-5 \\ \\ x=4\colon \\ 12-2y=16 \\ 2y=-4 \\ y=-2 \end{gathered}[/tex]
Now, graphing these points and the line that passes through them, we have:
The slope can be calculated using the two points in the formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-(-5)}{4-2} \\ m=\frac{-2+5}{2} \\ m=\frac{3}{2} \end{gathered}[/tex]
The y-intercept can be calculated using x = 0 in the equation or looking where the graph intersects the y-axis:
[tex]\begin{gathered} x=0\colon \\ -2y=16 \\ y=-8 \end{gathered}[/tex]
So the y-intercept is (0, -8).
