Final answer:
The equation for line d, which is perpendicular to line c (y = -6x - 3) and passes through the point (3, -3), is y = (1/6)x - 7/2.
Step-by-step explanation:
To find the equation of a line (line d) that is perpendicular to another line (line c) with the equation y = -6x - 3, we first need to determine the slope of line c. The slope of line c is -6. Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, the slope of line d will be the negative reciprocal of -6, which is 1/6.
Next, we plug the point (3, -3) and the slope 1/6 into the slope-intercept form equation y = mx + b to find the y-intercept b.
y = mx + b
-3 = (1/6)(3) + b
-3 = 1/2 + b
b = -3 - 1/2
b = -7/2
The equation for line d is y = (1/6)x - 7/2.