Find the slope-intercept form of an equation of the line perpendicular to the graph of x - 3y = 5 and passes through (0,6).

A. y = 1/3x + 2

B. y = 3x - 6

C. y = 1/3x - 2

D. y = - 3x + 6

the desired equation is y = - 3x + 6.

Step-by-step explanation:

1) Rewrite x - 3y = 5 in slope-intercept form: x - 5 = 3y, or y = (1/3) (x - 5)

2) Identify the slope of the given line. It is (1/3).

3) Find the slope of a line perpendicular to this one. It is the negative reciprocal of (1/3), or - 3.

4) Use the slope-intercept form of the equation of a straight line, y = mx + b, to determine the b value and thus the equation of the perpendicular line:

6 = - 3 (0) + b. Then b = 6, and the desired equation is y = - 3x + 6.