PSAT Algebra — lines on the grid: slope, intercepts and equations

Lines in the coordinate plane run through the whole Algebra domain of the PSAT/NMSQT, and a good share of those questions come with a graph or a table rather than an equation. This material trains the moves you need to go from any of those representations to the equation of a line and back.

You compute a slope from two points and keep the subtraction in the same order, including the double negative that catches many students. You find the x- and y-intercepts of a line written in standard form, read the slope of Ax + By = C without rewriting it, and turn a table of values into an equation by dividing the change in y by the change in x. You write the equation of a line through a given point that is parallel or perpendicular to another line, and you recognize horizontal and vertical lines from their points.

Several questions show the line itself, drawn on a coordinate grid with two marked points: you read the slope and intercept off the drawing, find where the line crosses the x-axis, or find where two drawn lines intersect. Context questions ask what the slope and the y-intercept mean for a kayak rental (cost per hour versus a fixed fee) and when a candle burning at a constant rate runs out.

The quiz has twelve multiple-choice questions with explanations that say why each wrong answer is tempting: an inverted slope, a lost sign, the intercept mistaken for the rate. The flashcards hold the formulas and rules, from the slope formula to the negative reciprocal. The printable written work asks for full equations and interpretations in your own words, as in the student-produced responses of the test, and one item uses the kayak graph. The oral exam lets you talk through a line problem step by step with an examiner who asks for your reasoning one question at a time.

The content is based on the College Board's published skill descriptions for the PSAT/NMSQT Math section (Algebra: linear functions and linear equations in two variables). It is independent practice, not produced or endorsed by the College Board.

• Compute the slope of a line from two points, a table, a graph or an equation in standard form
• Find the x- and y-intercepts of a line and interpret them in context
• Write the equation of a line through a point, parallel or perpendicular to a given line
• Read the equation of a line and the intersection of two lines from a coordinate grid
• Interpret the slope and y-intercept of a linear model such as a rental cost

Practice material written by Zestly, based on the College Board's skill descriptions for the digital PSAT/NMSQT Math section (Algebra: linear functions; linear equations in two variables — slope, intercepts, parallel and perpendicular lines, connections between tables, equations and graphs), as published on satsuite.collegeboard.org and in the Assessment Framework for the Digital SAT Suite.