Question

first graph the equations, and then mark the point of intersection.
$y = -\frac{1}{6}x + 3$
$y = -\frac{2}{3}x$
click to select
point e
line aa
line bb

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 \((-6, 4)\)