the graph of which of the following will be perpendicular to the graph of 4x- 3y= -12a. 4x+3y=12b. y=-3/4x-8c.y=3/4x+1d. 3x-4y=1

Answer:(b) y=-3/4x-8Step-by-step explanation:The graph that will be perpendicular to the graph 4x - 3y = -12If this equation is represented in form of the straight line equation y = mx + bit will change to 3y = 4x + 12therefore y = (4/3)x + (12/3)y = (4/3)x + 4which implies that m = 4/3 while b = 4However for the line that will be perpendicular to the graph, its slope m1 must be negative inverse of the slope of the initial graphThis is because m x m1 = -1therefore m1 = -1/mthis implies that the correct answer must have a slope of -1/(4/3) = -3/4The correct answer can then be analysed by expressing all options with y = mx + b(a) In form of y = m1x + b, 4x+3y=12 becomes y = -4/3x + 4 (m1 = -4/3: wrong)(b) In form of y = m1x + b, y=-3/4x-8 has m1 = -3/4 (correct)(c) In form of y = m1x + b, y=3/4x+1 has m1 = 3/4 (wrong)(d) In form of y = m1x + b, 3x-4y=1 becomes y = 3/4x - 1/4 (m1 = 3/4: wrong)