what is the slope of the line parallel to 2y=3x+6what is the slope of the line perpendicular to y=8x+24

Answer:Step-by-step explanation:The equation of a straight line is usually represented in the slope-intercept form, y = mx + cWhere c = y interceptm = slopeWe want to determine the slope of the line parallel to 2y=3x+6Rearranging 2y=3x+6 in the slope intercept form, it becomes2y/2 = 3x/2 + 6/2y = 3x/2 + 3The slope = 3/2If two lines are parallel to each other, the their slopes are equal.So the slope of the line parallel to 2y=3x+6 is 3/2To determine slope of the line perpendicular to y=8x+24Comparing y=8x+24 with the slope intercept form, y = m+ c,Slope, m = 8If two limes are perpendicular, then the product of the slopes is -1Let the slope of the perpendicular line to the one given by the above equation be m1. Therefore,8 × m1 = -18 m1 = -1m1 = -1/8,