The problem is to simplify the given equation $6y - 2 = 2x - 2$, find the x-intercept and y-intercept, and then graph the equation.

1. Problem Description

The problem is to simplify the given equation $6y - 2 = 2x - 2$, find the x-intercept and y-intercept, and then graph the equation.

2. Solution Steps

First, we simplify the equation:

$6y - 2 = 2x - 2$

Add 2 to both sides:

$6y = 2x$

Divide both sides by 6:

$y = \frac{2x}{6}$

$y = \frac{1}{3}x$

To find the x-intercept, we set $y = 0$:

$0 = \frac{1}{3}x$

$x = 0$

So, the x-intercept is $(0, 0)$.

To find the y-intercept, we set $x = 0$:

$y = \frac{1}{3}(0)$

$y = 0$

So, the y-intercept is $(0, 0)$.

Since both intercepts are at the origin $(0, 0)$, we need to find another point on the line.

Let's choose $x = 3$. Then:

$y = \frac{1}{3}(3)$

$y = 1$

So, the point $(3, 1)$ is on the line.

3. Final Answer

$y = \frac{1}{3}x$