Question

Find the acute angle between the lines. Round your answer to the nearest degree. 9x − y = 4, 8x + y = 6

Answer 1

Answer:

$\approx 13^\circ$

Step-by-step explanation:

Given two lines with the equations:

$9x - y = 4\\ 8x + y = 6$

First of all, let us learn the formula for finding the angle between the two lines with given equations:

$tan\theta = \dfrac{m_1-m_2}{1+m_1m_2}$

$m_1, m_2$ are the slopes of the two lines respectively.

Let us convert the given equation to point intercept form.

Point intercept form of a line is given as:

$y = mx+c$

$y = 9x-4\\y =-8x+6$

Comparing with slope intercept form, we get:

$m_1 = 9\\m_2 = -8$

Using the above formula:

$tan\theta =\dfrac{9 -(-8)}{1+9(-8)}\\\Rightarrow tan\theta = -\dfrac{17}{71}\\\Rightarrow \theta = -13.46^\circ$

Therefore, the acute angle between the two lines is $\approx 13^\circ$