How Do You Know if Two Lines are Parallel?

Note:

Parallel lines are lines that will go on and on forever without ever intersecting. This is because they have the same slope! If you have two linear equations that have the same slope but different y-intercepts, then those lines are parallel to one another!

Keywords:

definition
line
linear equation
parallel lines
same slope
parallel
equal slope

Background Tutorials

communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
- What's the Y-Intercept?
  
  When you have a linear equation, the y-intercept is the point where the graph of the line crosses the y-axis. In this tutorial, learn about the y-intercept. Check it out!
select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
- What Does the Slope of a Line Mean?
  
  You can't learn about linear equations without learning about slope. The slope of a line is the steepness of the line. There are many ways to think about slope. Slope is the rise over the run, the change in 'y' over the change in 'x', or the gradient of a line. Check out this tutorial to learn about slope!
Determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, ax + by = c, and y - y1 = m(x - x1)
- What's the Formula for Slope?
  
  When you're dealing with linear equations, you may be asked to find the slope of a line. That's when knowing the slope formula really comes in handy! Learn the formula to find the slope of a line by watching this tutorial.
- What's Slope-Intercept Form of a Linear Equation?
  
  When you're learning about linear equations, you're bound to run into the point-slope form of a line. This form is quite useful in creating an equation of a line if you're given the slope and a point on the line. Watch this tutorial, and learn about the point-slope form of a line!