Unit 2 of 6

Algebra

  • 13 lessons
  • Parts 13 to 38

Linear equations and linear functions are the largest single part of the SAT Math section. This unit solves linear equations, rearranges formulas, and recognizes equations with no solution or infinitely many.

It then reads and writes linear functions from graphs, tables and situations, with slope, intercepts, and parallel and perpendicular lines, solves systems of two linear equations in several ways, and finishes with linear inequalities and the regions they describe.

Every lesson is a pair of videos. The theory part explains the idea and the practice part works through problems. Each lesson page has the definitions and an example for every key term.

Linear Equations

  1. Solving Linear Equations

    How to solve a linear equation in one variable with steps that keep exactly the same solutions, how to clear fractions safely, and how to find a requested expression directly.

    Theory part 13Practice part 14

  2. Rearranging Formulas

    How to make any letter of a formula its subject using the same steps as for linear equations, while stating which divisors must be nonzero and handling the cases where they are zero.

    Theory part 15Practice part 16

  3. Equations with No or Infinitely Many Solutions

    Why a linear equation can have every allowed number or no number as a solution, how the leftover constant statement tells you which, and how to choose a constant that forces each case.

    Theory part 17Practice part 18

Functions and Lines

  1. Coordinates, Functions and Graphs

    How a function rule, a table of values and a graph describe the same input and output pairs, how to evaluate f at a number or an expression, and how to work back from an output to its inputs.

    Theory part 19Practice part 20

  2. Slope and Rate of Change

    How to compute the slope of a line from two points, what its sign and size say, how slope becomes a rate with units in a real situation, and why horizontal and vertical lines behave differently.

    Theory part 21Practice part 22

  3. Intercepts and Linear Models

    How to find the intercepts of a line, what the slope, the starting value and each intercept mean in a real situation, and why a linear model holds only on the inputs the situation allows.

    Theory part 23Practice part 24

  4. Writing the Equation of a Line

    How to write the equation of a line from a slope and a point, from two points, or from a graph, and how to move between slope-intercept, point-slope and standard form.

    Theory part 25Practice part 26

  5. Parallel and Perpendicular Lines

    How slopes tell you when two lines are parallel or perpendicular, why perpendicular slopes are negative reciprocals, and how horizontal and vertical lines fit the picture.

    Theory part 27Practice part 28

Linear Systems

  1. Systems of Equations by Graphs and Substitution

    What it means for an ordered pair to solve a system of two equations, how that pair appears as the intersection of two graphs, and how substitution finds it exactly.

    Theory part 29Practice part 30

  2. Systems of Equations by Elimination

    How to add multiples of two equations so that one variable cancels, why this keeps the solution set the same, and how a single combination can give an expression like x + y directly.

    Theory part 31Practice part 32

  3. Systems with One, No or Infinite Solutions

    How to tell from the equations alone whether two lines cross once, never meet or lie on top of each other, including systems whose coefficients contain an unknown constant.

    Theory part 33Practice part 34

Linear Inequalities

  1. Solving Linear Inequalities

    How to solve a linear inequality step by step, why the sign flips when you multiply or divide by a negative number, and how to read its boundary, endpoints and whole number answers.

    Theory part 35Practice part 36

  2. Graphing Inequalities and Feasible Regions

    How a shaded region in the plane stands for every pair that satisfies a set of linear inequalities, and how to decide whether a given point belongs to it.

    Theory part 37Practice part 38