Question

acute angle between the lines y=2x+3 & y=3x+7​

Answer 1

Answer:

hence required answer is 8.1° or 0.14 radias

Answer 2

Given,

Two lines:

y = 2x + 3,

y = 3x + 7.

To find,

The acute angle between them.

Solution,

When a line is in the form of the equation,

y = mx + c

then, m is said to be its slope.

If m₁ m₂ are the slopes of two lines, then the acute angle (θ) between them is given by

$\tan\theta=|\frac{m_1-m_2}{1+m_1m_2} |$     ...(1)

Here, the given equations are,

y = 2x + 3,

y = 3x + 7

It can be seen that the slopes of these lines are,

m₁ = 2

m₂ = 3

Substituting these values in the aforementioned formula (1), we get,

$\tan\theta=|\frac{2-3}{1+2\cdot3} |$

⇒ $\tan\theta=|\frac{-1}{1+6} |$

⇒ $\tan\theta=\frac{1}{7}$

⇒ $\theta=\tan^{-1}(\frac{1}{7} )$

⇒ θ = 8.13°.

Therefore, the acute angle between the given lines (y = 2x + 3) and (y = 3x + 7) is 8.13°.