The graph of which of the following will be perpendicular to the graph of 4x - 3y = - 12

a. 4x+3y=12

b. y=-3/4x-8

c. y=3/4x+1

d. 3x-4y=1

(b) y=-3/4x-8

Step-by-step explanation:

The graph that will be perpendicular to the graph 4x - 3y = - 12

If this equation is represented in form of the straight line equation y = mx + b

it will change to 3y = 4x + 12

therefore y = (4/3) x + (12/3)

y = (4/3) x + 4

which implies that m = 4/3 while b = 4

However for the line that will be perpendicular to the graph, its slope m1 must be negative inverse of the slope of the initial graph

This is because m x m1 = - 1

therefore m1 = - 1/m

this implies that the correct answer must have a slope of - 1 / (4/3) = - 3/4

The 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)