# Angle Between Lines

## Linear Functions – Angle Between Lines

If the acute angle $$\theta$$ between two straight lines $$y = m_1 x + A$$ and $$y = m_2 x + B$$, then
$$\tan{\theta} = \left|\frac{m_1 – m_2}{1+m_1 \times m_2}\right|$$

### Basic of Angle Between Lines

Find the acute angles between the lines $$y = -2x + 4$$ and $$y = 3x + 2$$, giving your answer to the nearest degree.

### Gradients for Angle Between Lines

Find the acute angles between the lines $$2y = x + 1$$ and $$2x – 3y = 4$$, giving your answer to the nearest degree.

### The Nearest Minute for Angle Between Lines

Find the acute angle between the lines $$2x+y+1=0$$ and $$x+y+4=0$$, correcting to the nearest minute.

### Two Points for Angle Between Lines

Find the acute angle between the line $$2x-5y+1=0$$ and the line joining $$(-1,2)$$ and $$(5,3)$$, correcting to the nearest minute.

### Angle Between Lines of Intersection of Exponential Graphs

Find the angle between the tangents drawn to the curve $$y_1 = e^{x}$$ and $$y_2 = e^{-x}$$ at their point of intersection.

### Angle Between Lines of intersection of Trigonometric Graphs

Find the acute angle between the curves $$y_1 = \sin{x}$$ and $$y_2 = \sin{2x}$$, at their point of intersection, where $$0 \lt x \lt 180^{\circ}$$, correcting to the neatest degree.

### Angle Between Lines for Finding Gradients

The acute angle between the lines $$2x-y-7=0$$ and $$y=mx+3$$ is $$25^{\circ}$$, find the value(s) of $$m$$, correct to 1 decimal place.