Final answer:
The equation of the line through point (12, 5) and parallel to the given line is y = (3/2)x - 13.
Step-by-step explanation:
The equation of the line through point (12, 5) and parallel to the line 3x - 2y = 20 can be found using the fact that parallel lines have the same slope. Since 3x - 2y = 20 is in slope-intercept form y = mx + b, where m is the slope, we can determine that the slope of the given line is 3/2.
Therefore, the equation of the parallel line can be written as y = (3/2)x + b, where b is the y-intercept. To find b, substitute the coordinates of the given point (12, 5) into the equation and solve for b. The equation becomes 5 = (3/2)(12) + b. Simplifying this gives 5 = 18 + b, so b = 5 - 18 = -13.
Therefore, the equation of the line through (12, 5) and parallel to 3x - 2y = 20 is y = (3/2)x - 13.