Final answer:
To find the equation of line d, we can use the negative reciprocal of line c's slope and the given point to determine the slope and y-intercept of line d. The equation of line d is y = 1/6x - 7/2.
Step-by-step explanation:
To find the equation of line d, we need to determine its slope and y-intercept. Since line d is perpendicular to line c, its slope is the negative reciprocal of line c's slope. The slope of line c is -6, so the slope of line d is 1/6.
Next, we can use the point (3, -3) to find the y-intercept of line d. Plugging in the values (x = 3, y = -3) and the slope (m = 1/6) into the equation y = mx + b, we can solve for b:
-3 = (1/6)(3) + b
-3 = 1/2 + b
-3 - 1/2 = b
-6/2 - 1/2 = b
-7/2 = b
Therefore, the y-intercept (b) is -7/2.
The equation of line d in y=mx+b form is y = 1/6x - 7/2.