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The equation of the line l passing through (4, 3) and parallel to d: 4x + 5y = 1 is l: 16x + by = c. What is the value of b? Please answer with steps.​

User Sorix
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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.

User Neini Amanda
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