Final answer:
To determine the equation of a line that is parallel or perpendicular to a given line and passes through a given point, we need to find the slope of the given line and use it to find the equation of the parallel or perpendicular line.
Step-by-step explanation:
To determine the equation of a line that passes through a given point and is parallel to another line, we need to find the slope of the given line and then use it to find the equation of the parallel line. In this case, the line parallel to 3x + 2y = 8 passes through (-1, 5). The slope of the given line is -3/2, so the equation of the parallel line is y - 5 = -3/2(x + 1), or y = -3/2x + 13/2.
To determine the equation of a line that passes through a given point and is parallel to another line, we need to find the slope of the given line and then use it to find the equation of the parallel line. In this case, the line parallel to 2y = 3x - 5 passes through (4, -2). The slope of the given line is 3/2, so the equation of the parallel line is y - (-2) = 3/2(x - 4), or y = 3/2x - 5.
To determine the equation of a line that passes through a given point and is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line and then use it to find the equation of the perpendicular line. In this case, the line perpendicular to 2x - 6y = 12 passes through (-2, 3). The slope of the given line is 1/3, so the slope of the perpendicular line is -3. The equation of the perpendicular line is y - 3 = -3(x + 2), or y = -3x - 3.