# 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.