Question

first graph the equations, and then mark the point of intersection.
$y = -dfrac{1}{6}x + 3$
$y = -dfrac{2}{3}x$

Explanation:

Step1: Set equations equal

To find the intersection, set $-\frac{1}{6}x + 3=-\frac{2}{3}x$.

Step2: Multiply by 6 to eliminate denominators

Multiply each term by 6: $-x + 18=-4x$.

Step3: Solve for x

Add $4x$ to both sides: $3x + 18 = 0$. Subtract 18: $3x=-18$. Divide by 3: $x = -6$.

Step4: Substitute x into one equation

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

Answer:

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