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.