SAT Algebra — parallel and perpendicular lines

Questions about linear equations in two variables on the SAT often turn on one relationship between two lines: they are parallel, or they are perpendicular. Both come down to slopes. Parallel lines have equal slopes; perpendicular lines, when neither is vertical, have slopes whose product is −1. This material trains the rule in every form the test asks for it.

You find the slope of a line parallel to one written in standard form, and the slope of a line perpendicular to one in slope-intercept form. You write the equation of a line through a given point that is parallel or perpendicular to a given line, find the y-intercept of a parallel line, and handle the special case of a line perpendicular to a horizontal line, which is vertical. You pick the one pair of equations that gives perpendicular lines out of four, avoiding the classic traps of opposite slopes without the reciprocal and reciprocal slopes without the sign change.

Constants make the questions harder: you find the value that makes a line in standard form parallel to a given line, and the value that makes two lines in standard form perpendicular. One question draws two lines on a coordinate grid and asks whether they are parallel, perpendicular, the same line or none of these; another builds a perpendicular through the endpoint of a segment. The link to systems of equations is made explicit: two distinct parallel lines never meet, so their system has no solution.

The quiz has twelve multiple-choice questions with worked explanations and a check of each answer. The flashcards collect the slope rules, the point-slope form and the tests for parallel and perpendicular lines. A calculator is allowed throughout the SAT Math section.

The material is based on the College Board's published description of the SAT Math section (Algebra domain: linear equations in two variables and systems of two linear equations). It is independent practice and is not produced or endorsed by the College Board.

• Find the slope of a line parallel or perpendicular to a given line, including one in standard form.
• Write the equation of a line through a point that is parallel or perpendicular to a given line.
• Decide whether two lines are parallel, perpendicular or neither from their equations or from a graph.
• Find a constant that makes two lines parallel or perpendicular.
• Connect distinct parallel lines with a system of equations that has no solution.

Practice material written by Zestly, based on the College Board's description of the digital SAT Math section, Algebra domain (skills: linear equations in two variables; systems of two linear equations in two variables).