Answer:
B = -¹⁵/₄
Explanation:
The slope of 7x = 2425 is 0, and the other two lines have non-zero slopes, so they must be the ones that are perpendicular.
(1) 3x + 4y = 5
(2) 5x + By = 13
1. Calculate the slope of Line (1)
3x + 4y = 5
Subtract 3x from each side: 4y = -3x + 5
Divide each side by 4: y = -¾x + ⁵/₄
The slope m₁ = -¾.
2. Calculate the slope of the perpendicular line
m₂ = -1/m₁
m₂ = ⁴/₃
3. Calculate the slope of Line (2)
5x + By = 13
Subtract 5x from each side: By = -5x + 13
Divide each side by B: y = (-5/B)x + 13/B
The slope m = -5/B.
4. Calculate the value of B
If Line (2) is the perpendicular line, then
⁴/₃ = -5/B
Multiply each side by B: (⁴/₃)B = -5
Multiply each side by 3: 4B = -15
Divide each side by 4: B = -¹⁵/₄
So, the value of B = -¹⁵/₄, and the equation of Line (2) is
5x - (¹⁵/₄)y = 13
The Figure below shows the graph of Line (1) in purple, and the graph of its perpendicular Line (2) in black.