Final answer:
To find the equation of a line parallel to the given line and passing through a given point (6, -2), we can use the point-slope form of a linear equation. The equation of the line in slope-intercept form is y = (2/3)x - 4.
Step-by-step explanation:
To find the equation of a line parallel to another line and passing through a given point, we need to know that parallel lines have the same slope. In this case, the given line has a slope of 2/3. We also have the point (6, -2).
So, we can use the point-slope form of a linear equation, which is: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values, the equation becomes: y - (-2) = (2/3)(x - 6). Simplifying, we get y + 2 = (2/3)(x - 6). To get the equation in slope-intercept form, we can rewrite it as: y = (2/3)x - 4.