first graph the equations, and then mark the point of intersection.\n$y = -\frac{1}{6}x + 3$\n$y =…

Explanation:

Step1: Set the two equations equal

To find the intersection point, set $y = -\frac{1}{6}x + 3$ equal to $y = -\frac{2}{3}x$. So we have the equation: $$-\frac{1}{6}x + 3 = -\frac{2}{3}x$$

Step2: Solve for (x)

First, add $\frac{2}{3}x$ to both sides to get: $$-\frac{1}{6}x+\frac{2}{3}x + 3=0$$ Convert $\frac{2}{3}x$ to sixths: $\frac{2}{3}x=\frac{4}{6}x$. Then: $$-\frac{1}{6}x+\frac{4}{6}x + 3=0$$ $$\frac{3}{6}x + 3=0$$ Simplify $\frac{3}{6}x$ to $\frac{1}{2}x$: $$\frac{1}{2}x + 3=0$$ Subtract 3 from both sides: $$\frac{1}{2}x=-3$$ Multiply both sides by 2: $$x = - 6$$

Step3: Find (y) by substituting (x)

Substitute $x = - 6$ into $y = -\frac{2}{3}x$: $$y=-\frac{2}{3}\times(-6)$$ $$y = 4$$

Answer:

The point of intersection is ((-6, 4))