Algebra 1
Every lesson explains the concept, works through examples, and gives you practice problems with full solutions. Work through them in order, or jump to the topic you need.
45 lessons
- How to Solve One-Step EquationsSolve one-step equations by doing the same inverse operation to both sides, with worked examples, common mistakes, and practice problems with full solutions.
- How to Solve One-Step InequalitiesSolve one-step inequalities the same way as equations, plus the one rule that changes: why the sign flips when you multiply or divide by a negative.
- How to Solve Two-Step EquationsSolve two-step equations by undoing addition first and multiplication second, with worked examples, common mistakes, and practice problems with full solutions.
- How to Solve Multi-Step EquationsSolve multi-step equations by distributing, combining like terms, then undoing operations in reverse order, with worked examples and practice problems.
- How to Solve Multi-Step InequalitiesSolve multi-step inequalities by distributing, combining like terms, and undoing operations in reverse order, including when to flip the inequality sign.
- Solving Equations with Variables on Both SidesSolve equations with variables on both sides by collecting variable terms on one side, plus how to recognize no solution and infinitely many solutions.
- How to Solve Literal Equations and Rearrange FormulasRearrange a formula to solve for any variable using the same inverse operations you use on numbers, with worked examples from geometry, physics, and finance.
- What Slope Is, and Why It Never Changes on a LineLearn what slope measures, how to find it with rise over run and the slope formula, and why similar triangles guarantee it is the same everywhere on a line.
- Slope-Intercept Form: y = mx + bUnderstand y = mx + b, what m and b each control, how to graph a line from it in two moves, and how to rewrite any linear equation into this form.
- Comparing Functions Across Tables, Graphs and EquationsHow to compare two functions given in different forms, build a linear function from a table or a description, and read the rate of change from each one.
- How to Graph Linear EquationsGraph a line three ways — from slope-intercept form, from intercepts, or from a table — and understand why every point on the line is a solution.
- Point-Slope Form: Writing a Line from One PointLearn point-slope form, why it is the slope formula rearranged, and how to use it to write a line's equation from a single point and a slope.
- How to Write the Equation of a Line from Two PointsFind a line's equation from any two points: compute the slope, substitute into point-slope form, then simplify — with worked examples and full solutions.
- Reading a Graph: Describing How Two Quantities ChangeHow to read a graph qualitatively — where it increases, decreases or stays flat, what steepness means, and how to sketch a graph from a story without any numbers.
- x-Intercepts and y-Intercepts: Finding Where a Line CrossesFind the x- and y-intercepts of any equation by setting the other variable to zero, why that works, and what intercepts mean in a real situation.
- Standard Form of a Linear Equation: Ax + By = CWhat standard form is, when it beats slope-intercept form, how to convert between the two, and how to find the slope without rearranging.
- Function Notation: What f(x) Actually MeansUnderstand f(x) as a name and an input rather than multiplication, how to evaluate it, and how to read statements like f(3) = 7 in context.
- Domain and Range: The Inputs and Outputs of a FunctionWhat domain and range mean, how to find them from a graph, a table or an equation, and why some inputs have to be excluded.
- Rate of Change: Slope With Units AttachedWhat average rate of change means, how it relates to slope, how to compute it from a table or a function, and how to read its units and sign.
- Linear vs Nonlinear Functions: How to Tell Them ApartFour reliable tests for deciding whether a relationship is linear — from its equation, its table, its graph, or its rate of change.
- Solving Systems of Linear EquationsSolve a system by graphing, substitution or elimination, why the solution is the intersection point, and how to spot systems with none or infinitely many.
- Scatter Plots and the Line of Best FitRead a scatter plot, describe its association, draw and use a line of best fit, and understand why correlation does not prove causation.
- Adding and Subtracting PolynomialsWhat a polynomial is, how to read its degree and leading coefficient, why only like terms combine, and why subtracting means distributing the minus sign to every term.
- Exponential Functions: Growth by a Constant FactorHow to tell an exponential situation from a linear one, what the start value and growth factor mean, and why exponential growth eventually passes any straight line.
- Arithmetic and Geometric SequencesHow to tell an arithmetic sequence from a geometric one, how to write each recursively and explicitly, and why the explicit rules are linear and exponential functions.
- Exponential Growth and Decay ModelsHow to build an exponential model from a description, a table or two points, what each parameter means in context, and how to read a growth curve's key features.
- Graphing Linear Inequalities in Two VariablesHow a linear inequality splits the plane into a half-plane of solutions, when the boundary line is solid and when it is dashed, and how to shade a system of inequalities.
- How to Solve Compound Inequalities (AND and OR)Solve compound inequalities joined by AND or OR, graph the solution on a number line, and tell which combinations give no solution or every number.
- How to Solve Absolute Value EquationsSolve absolute value equations by splitting into two cases, why two answers appear, when there is no solution, and how absolute value inequalities differ.
- How to Solve Absolute Value InequalitiesSolve absolute value inequalities by thinking in distances: less than gives one stretch of the number line, greater than gives two rays pointing away.
- Multiplying Polynomials: The Box Method and FOILHow to multiply polynomials with the distributive property, why the box method never misses a term, where FOIL comes from, and the two special products to know.
- Factoring QuadraticsHow to factor a quadratic by finding a pair that multiplies to c and adds to b, when to pull out a common factor first, and how to spot the two special patterns.
- Parallel and Perpendicular Lines: The Slope RulesParallel lines have equal slopes and perpendicular lines have negative reciprocal slopes — why both rules are true, and how to write equations using them.
- Piecewise, Absolute Value and Step FunctionsHow to read, evaluate and graph a function built from several rules, why endpoints need open and closed dots, and how absolute value and step functions fit the pattern.
- Rational Exponents and RadicalsWhy a power of one half has to mean a square root, how to read the top and bottom of a fractional exponent, and how to switch between radical and exponent form.
- Solving Equations by Graphing Both SidesWhy the x-coordinates where y = f(x) and y = g(x) cross are the solutions of f(x) = g(x), and how to approximate them with a graph, a table and successive narrowing.
- Solving Quadratic Equations by FactoringSolve quadratics by factoring using the zero product property, why the equation must equal zero first, and how to factor the common trinomial patterns.
- Completing the Square, Step by StepLearn completing the square: why the method works geometrically, how to handle a leading coefficient, and how it produces vertex form and the quadratic formula.
- The Quadratic Formula: How and Why It WorksLearn the quadratic formula, where it comes from, and how to use it to solve any quadratic equation, with worked examples and practice problems.
- Graphing Quadratic Functions: Vertex, Axis and InterceptsHow to find the vertex and axis of symmetry of a parabola, why the axis sits at -b over 2a, and what each of the three forms of a quadratic reveals at a glance.
- Systems of a Line and a Parabola or CircleHow to solve a system of one linear and one quadratic equation by substitution and by graphing, and why such a system has two, one or no solutions.
- Transformations of Functions: Shifts, Stretches and ReflectionsWhat each change to f(x) does to its graph, why a change inside the parentheses moves the graph the opposite way, and how to read the constants off a picture.
- Inverse Functions: Undoing What a Function DoesHow to find an inverse by swapping x and y, why the graph reflects across the line y = x, and how the horizontal line test decides whether an inverse is a function.
- Units, Quantities and AccuracyHow units guide a multi-step problem and catch errors, what the units of each part of a formula mean, how to define a quantity, and how many digits an answer deserves.
- Writing Equations and Constraints from SituationsHow to turn a situation into an equation or inequality and solve it, why some solutions are not viable, and how a system of inequalities shows every option that works.