find the acute angle between $y = 5 x + 6$ and $y = x$

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Solution

$y = 5 x + 6$

$\Rightarrow m_{1} = 5$

$y = x$

$\Rightarrow m_{2} = 1$

Angle between the lines is given by

$tan θ = ∣ ∣ ∣ \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} ∣ ∣ ∣$

$= ∣ ∣ ∣ \frac{5 - 1}{1 + 5 (1)} ∣ ∣ ∣$

$= \frac{4}{1 + 5}$

$= \frac{2}{3}$

$∴ θ = {tan}^{- 1} (\frac{2}{3})$ .

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