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Find the distance between the pair of parallel lines with the given equations.

y=5 x-22

y=5 x+4

User NMGod
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To find the distance between a pair of parallel lines with the given equations, we can use the formula:

Distance = |c₁ - c₂| / √(a² + b²),

where c₁ and c₂ are the constants on the right-hand side of each equation, and a and b are the coefficients of x and y, respectively.

For the given equations:

y = 5x - 22 (equation 1)

y = 5x + 4 (equation 2)

Comparing the equations, we can see that both have the same coefficient of x (5), indicating that the lines are parallel.

Now, let's calculate the distance between the lines:

c₁ (equation 1) = -22

c₂ (equation 2) = 4

a = coefficient of x = 5

b = coefficient of y = 1

Plugging these values into the formula, we get:

Distance = |(-22) - 4| / √(5² + 1²)

= |-26| / √(25 + 1)

= 26 / √26

= 26 / √(2 * 13)

= 26 / (√2 * √13)

= 26 / (√2 * √13) * (√2 / √2) [Rationalizing the denominator]

= (26√2) / (2√13)

= 13√2 / √13

= 13√2 / √13 * (√13 / √13) [Rationalizing the denominator]

= (13√26) / 13

= √26

Therefore, the distance between the pair of parallel lines y = 5x - 22 and y = 5x + 4 is √26 units.

User KennyHo
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