How Do You Know if Two Lines are Parallel?

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

  • Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

      • What is the Coordinate Plane?What is the Coordinate Plane?

      What is the Coordinate Plane?

      You can't graph a function or plot ordered pairs without a coordinate plane! Learn about the coordinate plane by watching this tutorial.

  • Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

      • What's the Formula for Slope?What's the Formula for Slope?

      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 Does the Slope of a Line Mean?What Does the Slope of a Line Mean?

      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!

      • What's Slope-Intercept Form of a Linear Equation?What's Slope-Intercept Form of a Linear Equation?

      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!

  • Graph linear and quadratic functions and show intercepts, maxima, and minima.

      • What's the Y-Intercept?What's the Y-Intercept?

      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!