Linear equations
Find unknown values, connect slope with rate of change, and explain why two lines intersect.
- Solve one-variable linear equations
- Interpret y = mx + b
- Compare equations, tables, and graphs
GENIUS.NYC · Grades 6–8 Learning
Grade 8 Mathematics
Build confidence with linear equations, functions, exponents, and right-triangle geometry. Learn the reasoning, try worked examples, and check your understanding.
Grade 8 pathways
Four big ideas worth mastering
Each topic starts with a clear concept and a practical question. Choose one area, then try the related practice questions.
Functions
Recognize a rule that assigns one output to each input, and compare relationships.
- Evaluate function rules
- Read input-output tables
- Compare rates of change
Exponents
Use exponent rules and powers of ten to understand very large and very small values.
- Multiply powers of the same base
- Interpret negative exponents
- Write scientific notation
Right-triangle geometry
Apply the Pythagorean theorem to calculate missing side lengths and distances.
- Identify the hypotenuse
- Use a² + b² = c²
- Check a solution for reasonableness
Learn the method
Four worked examples
Follow the steps, then try a related question in the interactive practice section.
Solve a linear equation
Find x: 3x + 5 = 20.
1. Subtract 5 from each side: 3x = 15.
2. Divide by 3: x = 5.
Check: 3(5) + 5 = 20.
Use a function rule
A pattern follows y = 2x + 1. Find the output when x = 4.
1. Replace x with 4: y = 2(4) + 1.
2. Simplify: y = 8 + 1 = 9.
Check: Each input has exactly one output under this rule.
Multiply powers
Simplify: 2³ × 2⁴.
1. Keep the same base, 2.
2. Add exponents: 2³⁺⁴ = 2⁷.
Result: 2⁷ = 128.
Find a missing side
A right triangle has legs of 6 and 8 units. Find its hypotenuse.
1. Use a² + b² = c².
2. 6² + 8² = 36 + 64 = 100.
Result: c = √100 = 10 units.
GENIUS interactive practice
Try it. Check it. Learn why.
Select one of four areas. Each includes three original questions with instant explanations and a score summary.
Question 1 of 3
Loading question…
Choose an answer to see why it works.
Help students explain their thinking.
Try: “How do you know that?” “What changes when x increases?” and “Can you check the answer using another method?”
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