Final answer:
To find the equation of a parallel line through a given point, use the same slope as the original line. For the line parallel to y = -\(\frac{2}{3}\)x + 12 and passing through (6, 3), the slope-intercept form is y = -\(\frac{2}{3}\)x + 7.
Step-by-step explanation:
To find the equation of the line that is parallel to the given line y = -\(\frac{2}{3}\)x + 12 and passes through the point (6, 3), we need to use the same slope because parallel lines have the same slope. The slope of the given line is -\(\frac{2}{3}; hence, the new line will have the same slope. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We already have the slope m = -\(\frac{2}{3}, now we just need to find b by plugging the point (6, 3) into the slope-intercept equation:
3 = -\(\frac{2}{3})(6) + b
3 = -4 + b
b = 3 + 4
b = 7
Therefore, the equation of the line is y = -\(\frac{2}{3}\)x + 7.