Hi duasara! It is my pleasure to answer this question for you with step-by-step instruction.
Okay, two lines are parallel if they have the same slope. The equation of line d is 4x + 5y = 1. Solving for y, we get:
5y = -4x + 1
y = (-4/5)x + 1/5
So the slope of line d is -4/5.
Since line l is parallel to line d, it also has a slope of -4/5. The equation of line l is given as 16x + by = c. Solving for y, we get:
y = (-16/b)x + c/b
Comparing this with the equation y = (-4/5)x + 1/5 for line d, we see that the slope of line l is -16/b, which must equal -4/5. Therefore:
-16/b = -4/5
Multiplying both sides by -5b, we get:
80 = 4b
b = 20
Therefore, the value of b is 20.