# Find Equation of a Line from a Graph

Examples on how to find the equations of lines given their graphs. Examples and exercises are presented along with their detailed solutions and answers.

These following are reviews of formulas for slopes and equations of lines and are therefore used to solve the examples below.

- The slope \( m \) of a line with rise \( \Delta y \) corresponding to a run \( \Delta x \) is given by \[ m = \dfrac{\Delta y }{\Delta x} \]
- The slope \( m \) of a line through two points with coordinates \( (x_1,y_1) \) and \( (x_2,y_2) \) is given by \[ m = \dfrac{y_2 - y_1}{x_2 - x_1} \]
- The equation of a line that passes through the point \( (y_0 , x_0) \) and has slope \( m \) is given by \[ y - y_0 = m(x - x_0)\]
- The equation of a line with the y - intercept at \( (0 , b) \) and has slope \( m \) is given by \[ y = m x + b \]
- The equation of a horizontal line through the point \( (x_0 , y_0) \) is given by \[ y = y_0 \]
- The equation of a vertical line through the point \( (x_0 , y_0) \) is given by \[ x = x_0 \]
- The slopes \(m_1\) and \( m_2 \) of two perpendicular lines are related as follows \[ m_1 \cdot m_2 = -1 \]
- The slopes \(m_1\) and \( m_2 \) of two parallel lines are related as follows \[ m_1 = m_2 \]

## Examples with Detailed Solutions
Example 1 Graph of line with points
Example 2 Graph of line given run and rise
Example 3 Graph of line given run and fall
Example 4 Graph of horizontal line
Example 5 Graph of vertical line
Example 6 Graph of perpendicular line
## Exercises with Answers
Find the equations of the lines \(L_1\), \( L_2 \), \( L_3 \) and \( L_4 \) such that \(L_2 \) is parallel to \( L_1 \), \(L_3 \) is perpendicular to \(L_1\) and \( L_4 \) is a horizontal line.
- Equation of \(L_1\) : \( y = 2 x + 4 \)
- Equation of \(L_2\) : \( y = 2x - 2.5 \)
- Equation of \(L_3\) : \( y = - \dfrac{1}{2} x - \dfrac{7}{2} \)
- Equation of \(L_4\) : \( y = - 5 \)
## More References and Links to Equations and Slopes of LinesEquations of Lines in Different Forms.Equation of Line Questions with Solutions. Slopes of Parallel Lines Questions. Slopes of Perpendicular Lines Questions. slopes |