Final answer:
The equation of a line parallel to 3x + 5y = 10 that passes through the point (2,2) is found by using the slope of the given line and employing the point-slope form. The resulting equation after simplification and conversion should be 3x + 5y = 30, which does not match any of the provided options.
Step-by-step explanation:
To find the equation of a line parallel to another line, you must first understand that parallel lines have the same slope. The original equation given is 3x + 5y = 10. To find its slope, we can rearrange it into slope-intercept form (y = mx + b), where m is the slope.
Rewriting 3x + 5y = 10 into y = -⅓x + 2, we find that the slope (m) is -⅓. A parallel line will have the same slope but different y-intercept. Now, using the point (2,2), we employ the point-slope form of the equation, y - y1 = m(x - x1), which translates into y - 2 = -⅓(x - 2).
Simplifying, we get: y = -⅓x + ⅓(2) + 2. Simplified further, y = -⅓x + 4 + 2, hence y = -⅓x + 6. Converting back to standard form: 3x + 5y = 3x + 5(-⅓x + 6) = 3x - 3x + 30 = 30. So, the equation is 5y = 30, or 3x + 5y = 30. None of the provided choices match this equation exactly.