Given the function:
[tex]y=-\frac{2}{3}x+4[/tex]It's required to graph the function by joining at least 3 points.
Let's select the points x = -3, x = 3, and x = 9.
Substituting x = -3:
[tex]y=-\frac{2}{3}\cdot(-3)+4[/tex]Operating:
[tex]\begin{gathered} y=-\frac{-6}{3}+4 \\ y=2+4 \\ y=6 \end{gathered}[/tex]The first point is (-3,6)
Substitute x = 3:
[tex]y=-\frac{2}{3}\cdot3+4[/tex]Calculating:
[tex]\begin{gathered} y=-\frac{6}{3}+4 \\ y=-2+4 \\ y=2 \end{gathered}[/tex]The second point is (3,2)
Now for x = 9:
[tex]\begin{gathered} y=-\frac{2}{3}\cdot9+4 \\ y=-\frac{18}{3}+4 \\ y=-6+4 \\ y=-2 \end{gathered}[/tex]The third point is (9,-2).
Plotting the three points and joining them with a line, we get the following graph:
