Math 1 · Unit 4 · Lesson 1
Parallel Lines Share a Slope
Parallel lines never cross. On a graph that happens for one reason: they have the same slope, the same steepness and direction, but different y-intercepts. Same m, different b. It is the family of lines again: slide a line up or down and you get a parallel one. Then the skill: write a line parallel to a given line through a given point.
The big idea
Parallel lines never cross, and on a graph that is a statement about slope: two lines are parallel exactly when they have the same m and a different b. Same steepness, same direction, different starting point. Nothing new is added to what a line is; it is the family of lines from Unit 3 sorted by slope, where every slide of b gives another parallel member. So writing a parallel line through a point is two moves you already know: keep the slope, and put the point in to find the new b. Vertical lines are parallel to each other by sight, since they have no slope to compare, and horizontal lines all share slope 0.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with the parallel rule, the family connection, the two moves for a parallel line through a point, the special cases, and a worked example. Plus a worksheet with grids and an answer key, and a short lesson plan.