SAT Algebra — reading lines from graphs and tables

Many SAT Algebra questions do not give a formula at all. They show a line in the xy-plane, a graph of a real-world model with labeled axes, or a few values of a linear function, and ask for the equation, a value or the meaning of a number. This material trains exactly that reading, with a drawing on most questions.

From plotted lines you find the slope from two marked points and the y-intercept from one of them, choose the equation that matches, check a standard-form equation against both intercepts, evaluate a function shown only by its graph, and solve f(x) = k from the picture without confusing the input with the output. One graph has no numbers at all: you decide the signs of the slope and the y-intercept from the direction of the line and where it crosses the y-axis.

Two graphed models put the numbers in context. A gym membership cost that grows month by month asks for the best interpretation of the slope and for a prediction the graph does not show directly; a tank that drains to empty asks what the horizontal intercept means and how much water is left after a given time. Short lists of values of a linear function, written as a small grid of x and f(x) values, ask for the equation, a missing value, and the meaning of the constant term of a snow-depth model.

The quiz has twelve multiple-choice questions with worked explanations. Distractors come from the usual slips: run over rise instead of rise over run, the y-coordinate of a marked point taken for the intercept, the slope read as a fixed fee, the amount drained reported instead of the amount left, a step of the wrong size in a list of values. The flashcards collect the rules for slope, intercepts and interpretation in context. 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 linear functions, including making connections between algebraic, graphical and tabular representations and interpreting them in context). It is independent practice and is not produced or endorsed by the College Board.

• Find the slope and y-intercept of a plotted line from two marked points and choose its equation.
• Check an equation in standard form against the intercepts of a graph.
• Decide the signs of m and b from the shape and position of a line.
• Interpret the slope, the intercepts and a point of a graphed linear model in context, with units.
• Write a linear function from a short list of its values and use it to find a missing value.

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; linear functions — connections between algebraic, graphical, tabular and contextual representations).