Final answer:
To find the equation of a line that is parallel to another line and passes through a given point, we use the fact that parallel lines have the same slope. The slope-intercept form of the given line is y = (3/2)x - 6. The equation of the line passing through (-8,2) is y = (3/2)x + 14.
Step-by-step explanation:
To find the equation of a line that is parallel to another line and passes through a given point, we need to use the fact that parallel lines have the same slope. The given line, 3x-2y=12, can be rearranged to slope-intercept form, which is y = mx + b, by solving for y. The slope-intercept form is y = (3/2)x - 6. Since the parallel line has the same slope, the equation of the line passing through (-8,2) is y = (3/2)x + b.
To find the value of b, we substitute the coordinates of the point (-8,2). Therefore, 2 = (3/2)(-8) + b. Solving this equation, we get b = 14. Finally, the equation of the line is y = (3/2)x + 14.