# Find the Equation of a Line

A series of free Basic Algebra Lessons.

In this lesson, we will learn

• How to find the equation of a graphed line?
• Parallel and Perpendicular Lines

### Finding the Equation of a Graphed Line

Sometimes we’ll be given a graph of a line, and told to find the equation. There are many methods of finding the equation of a line with only a graph such as finding the slope and a point or finding two points. In order to understand finding the equation of line with its graph, one should understand the different forms of an equation of a line, especially point-slope and slope-intercept form.

How to determine the equation of a line in point-slope form and slope-intercept from the graph of a line?
y - y1 = m(x - x1)

How to determine a linear equation in point-slope form and slope-intercept form given the slope of the line and a point on the line?
Example:
A line has a slope of 2/3 and passes through (-4,6)
Write the line in point-slope form.
Write the line in slope intercept form.

How to determine the equation of a line in standard form given two points?
It shows how to determine the equation using slope-intercept form and then how to write the equation in standard form.
Example:
Determine the equation of the line passing through (-1,1) and (1,7). Write the line in standard form.

How to determine the equation of a line in slope intercept form given the graph of a line?

How to determine the equation of a line in point slope form and slope intercept form given two points on the line?
Example:
Determine he equation of the line passing through (1,1) and (5,-1)

### Equations of Parallel and Perpendicular Lines

There are special rules to help us find the equation of a line given an equation of a line that is parallel or perpendicular to it. Parallel and perpendicular lines have related slopes. Parallel lines have equivalent slopes and perpendicular lines have negative inverses of their slopes. To fully understand and apply this concept, we should be familiar with the slope and the slope-intercept form of an equation.

Determine if two lines are parallel or perpendicular.
Determine the equation of lines that are parallel or perpendicular.

Parallel lines are two lines that never intersect. Two lines are parallel if they have the same slope and different y-intercepts.

Perpendicular lines are two lines that intersect and form a right angle. Two lines are perpendicular if the product of the slopes is -1.

Example:
Determine if the two lines are parallel, perpendicular or neither.

Equations of lines that are parallel or perpendicular to a given line, using slope-intercept (y=mx+b) form
Topics include: finding the equation of a line given a point on the line and a line that is parallel to it, and finding the equation of a line given a point on the line and a line that is perpendicular to it.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.