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What Is the Linear Equations?(With Examples)

A linear equation is an algebraic equation where each term is either a constant or the product of a constant and a single variable. When graphed, it forms a straight line. The name "linear" comes from the fact that these equations always create straight lines.

Grades 7-8 (Pre-Algebra)Key Stage 3 (Year 7-9)Årskurs 7-8

📖Definition

📐Formula

y = mx + b (slope-intercept form)

In this form: m represents the slope (steepness) of the line, b represents the y-intercept (where the line crosses the y-axis), and x and y are variables.

📝Step-by-Step Guide

Simplify both sides

Combine like terms and distribute any parentheses on each side of the equation.

Move variable terms to one side

Add or subtract to get all variable terms on one side of the equation.

Move constant terms to the other side

Add or subtract to get all constants on the opposite side from the variable.

Isolate the variable

Divide or multiply both sides to solve for the variable.

⚠️Common Mistakes to Avoid

Forgetting to perform the same operation on both sides
Sign errors when moving terms across the equals sign
Not distributing multiplication over parentheses correctly
Confusing slope and y-intercept in slope-intercept form

✏️Practice Problems

Easy

Solve 3x + 7 = 22

Answer: x = 5

Medium

Solve 2(x - 3) = 4x + 6

Answer: x = -6

Hard

Solve (2x + 1)/3 = (x - 2)/2

Answer: x = -8

Printable Linear Equations practice

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Worked Examples

Solve 3x + 7 = 22 Step by Stepeasy

Solve Linear Equation Step by Stepmedium

Systems of Equations Graphing Linear Equations Understanding Slope Linear Inequalities

Curriculum Alignment

CommonCore (8.EE.C.7)KS3

Classroom assessment context

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