Tyler Wallace's "Beginning and Intermediate Algebra: Section 2.5: Graphing - Parallel and Perpendicular Lines"
Read this section. Parallel lines never intersect, which is good to know if you are looking for an intersection! The shortest distance from a line to something else is perpendicular to the line. The slopes for parallel and perpendicular lines have simple relationships to each other (which you should memorize!).
Click https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2011/12/SAYLOR-MA001-TEXT.pdf link to open resource.