Question

I. Find the angle between the following straight lines.
y = 4 - 2x, y = 3x + 7​

Answer 1

Answer:

The angle between the lines 2x+y+4=0 and y-3x=7 is equal to π/4. M2 - the slope of the line y-3x = 7 is equal to 3.

Answer 2

The answer is 45°

Given: y = 4 - 2x _ Line (1)

           y = 3x + 7​ _ Line (2)

To find: Angle between Line (1) and Line (2)

Solution: To find the angle between given lines we will use the formula

⇒ tan θ = $| \frac{m_{1} - m_{2} }{1 + m_{1} m_{2} } |$   where m₁, m₂ are slopes of Line(1) and Line(2)

Now find slopes of Line (1) and Line (2)

If we observe given lines both are in the form of y = mx + c  

As we know slope line y = mx + c  is m

⇒ slope of line (1)  y = -2x +c , m₁ = -2

⇒ slope of line (2)  y = 3x + 7,  m₂ = 3

Now substitute m₁ = -2 and m₂ = 3 in formula

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

⇒  tan θ =  $| \frac{-2 - 3 }{1 + (-2) (3) } |$

⇒  tan θ =  $| \frac{-5 }{1 -6 } |$  

⇒  tan θ = $| \frac{-5 }{-5} |$    

⇒  tan θ = 1                

⇒  tan θ = tan 45°    [ ∵ tan 45° = 1 ]    

⇒  θ = 45°  

Therefore, angle between given lines is 45°

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