Linear Equations Lab

Attention Activity • Page 1

What's in this lesson: intro moves, two checkpoints, graph links, and a short scored assessment.
Why this matters: linear equations help you compare costs, rates, and unknown values fast.

Quick experiment: If one side loses 3, what must the other side do to stay fair?

⚖️ Keep it balanced

Can you keep the balance?

Think of an equation as a balance scale. Tap the move and watch both sides change together. The goal is to uncover the value of x without breaking equality.

Hook: both sides start equal, so every move must be matched.

x+ 3

7

Equation shown: x + 3 = 7

Page 2

What makes an equation linear?

A linear equation keeps the variable to the first power. That means no x² and no variable in the denominator. In one variable, your job is still the same: isolate the unknown.

Variable
x is the unknown value.

Equals sign
Both sides match.

Linear clue
Only first-power variables appear.

Spot the pattern

2x + 5 = 17
linear

x² + 2 = 10
not linear

Use the examples as a visual test: straight-line algebra keeps x un-squared.

Knowledge Check

Which statement best matches a linear equation?

Page 3

Solving one-step and two-step equations

Use inverse operations in reverse order. Undo addition or subtraction first, then undo multiplication or division so x stands alone.

x + 6 = 14 → subtract 6 → x = 8
3x - 2 = 10 → add 2 → 3x = 12 → divide by 3 → x = 4

Click to reveal one valid move at a time.

Start: 4x + 1 = 13

This visual ladder mirrors the order of inverse operations.

Knowledge Check

Solve the equation: 5x = 35

Quick cue: picture 35 split into 5 equal groups. Each group is x.

Page 4

From equation to graph

Many linear equations can be written as y = mx + b. The slope m tells how steep the line is. The intercept b tells where the line starts on the y-axis.

Slope: rise over run.
Intercept: where the line crosses y.

For y = 2x + 1, start at 1 on the y-axis, then rise 2 and run 1.

Mini graph story

Sample points (0,1), (1,3), and (2,5) line up because the rate of change stays constant.

Summary

Key Takeaways

Balance matters: whatever you do to one side of an equation, do to the other.

Inverse operations help: subtract added terms and divide multiplied terms to isolate the variable.

Linear forms connect ideas: equations like y = mx + b show both algebra and graph behavior.

Check your solution: substitute your answer back into the original equation.

Assessment Intro

Ready for the assessment?

You will answer 4 multiple-choice questions. Choose one answer per question. You will see only your final score at the end.

Use scratch work if helpful.
Each question has exactly 4 options.
You must answer the current assessment question before moving to the next one.

Assessment Q1

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Assessment Q2

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Assessment Q3

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Assessment Q4

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Results

Your assessment results

Final score

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Sources used
OpenStax Algebra and Trigonometry materials on linear equations and slope-intercept form; Khan Academy lessons on one-step equations, two-step equations, and slope-intercept form; CCSS-aligned algebra guidance on solving linear equations in one variable.