Given points that two lines go through or the graph of each line, classify the lines as parallel, perpendicular, or neither.

The slopes of parallel lines are equal, and the slopes of perpendicular lines are opposite reciprocals. This is a worked example of determining whether given lines are parallel or …

We are asked which of these lines are parallel. So parallel lines are lines that have the same slope, and they're different lines, so they never, ever intersect.

A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line). This article reviews all three cases.

Parallel lines never intersect, and perpendicular lines intersect at a 90 degree angle. Learn how to identify parallel and perpendicular lines.

Use multiple representations including mappings, tables, graphs, verbal description, and equations (only when linear) of two functions to compare the functions and draw conclusions.

So just to start off with, if we're dealing with systems of linear equations in two dimensions, there's only three possibilities that the lines or the equations can have relative to each other.

Experimentally verify the effect of geometric translations on segment length, angle measure, and parallel lines.

Calculating slope from tables Positive & negative slope Worked example: slope from graph Parallel & perpendicular lines from graph

If slopes are the same then the lines are either equivalent (both equations describe the same line) or parallel (and thus do not intersect). Two lines with different slopes will always intersect.