Before we graph the given equation, let's convert it to slope-intercept form first. Here are the steps.
1. Subtract 5 on both sides of the equation.
[tex]\begin{gathered} 5+3y-5=x-5 \\ 3y=x-5 \end{gathered}[/tex]2. Next, divide both sides of the equation by 3.
[tex]\frac{3y}{3}=\frac{x}{3}-\frac{5}{3}\Rightarrow y=\frac{1}{3}x-\frac{5}{3}[/tex]We have converted the equation to slope-intercept form.
The slope is 1/3 and the y-intercept is -5/3 or -1.67.
To complete the given coordinate, simply replace "x" with the given x-coordinate and solve for y in the slope-intercept form.
Let's start with (2, ?) which is x = 2.
[tex]\begin{gathered} y=\frac{1}{3}(2)-\frac{5}{3} \\ y=\frac{2}{3}-\frac{5}{3} \\ y=-\frac{3}{3} \\ y=-1 \end{gathered}[/tex]At x = 2, y = -1. Completing the first coordinate, we have (2, -1).
Next, at x = -1.
[tex]\begin{gathered} y=\frac{1}{3}(-1)-\frac{5}{3} \\ y=\frac{-1}{3}-\frac{5}{3} \\ y=\frac{-6}{3} \\ y=-2 \end{gathered}[/tex]Completing the second coordinate, we have (-1, -2).
Lastly, at x = -4:
[tex]\begin{gathered} y=\frac{1}{3}(-4)-\frac{5}{3} \\ y=\frac{-4}{3}-\frac{5}{3} \\ y=\frac{-9}{3} \\ y=-3 \end{gathered}[/tex]Completing the third coordinate, we have (-4, -3).
The graph of this equation is shown below:
