Final answer:
The equation of a line parallel to 3x - 4y = -17 passing through (-3, 2) is not provided in the options. It should have the same slope as the given line; however, the correct equation with that slope and through the given point is not listed.
Step-by-step explanation:
The student is asking to find the equation of a line that is parallel to the given line 3x - 4y = -17 and passes through the point (-3, 2). The slope of the given line can be found by rearranging the equation to the slope-intercept form (y = mx + b) where 'm' is the slope. Converting 3x - 4y = -17 to slope-intercept form gives y = (3/4)x + 17/4, so the slope (m) is 3/4. A parallel line must have the same slope. Thus the new line will have the equation y = (3/4)x + b. To find 'b', we substitute the point (-3, 2) into the equation: 2 = (3/4)(-3) + b, which simplifies to 2 = -9/4 + b. Solving for 'b' gives b = 2 + 9/4 = 17/4. Therefore, the equation of the new line is y = (3/4)x + 17/4 or in standard form 3x - 4y = -17 + (4)(17/4) = 0. However, this results in the equation of the original line. Since there are no such options that give us 0, and the provided options don't make sense for a parallel line with this specific point, the correct equation of the line that is parallel to the given line passing through (-3, 2) is not listed among provided answers.