Slope and line equations practice

Understand the method

For two points, m = (y₂ − y₁)/(x₂ − x₁) when the denominator is nonzero. Point-slope form y − y₁ = m(x − x₁) then describes the nonvertical line through one point with that slope.

Worked example, step by step

Find the line through (2, 3) and (6, 11).

1. Compute slope: (11 − 3)/(6 − 2) = 8/4 = 2.
2. Use the first point: y − 3 = 2(x − 2).
3. Expand and rearrange: y = 2x − 1.
4. Check the other point: 2(6) − 1 = 11. The intercept is −1, not the first point’s y-coordinate.

A mistake to watch for

A vertical line has an undefined slope because horizontal change is zero. It is written x = constant, not y = mx + b with an extremely large finite slope.

Try it yourself: three questions

Write an answer before opening the explanation. For calculations, keep your units and intermediate steps; for concepts, state the reason for your choice.

Build your next practice session

Mark the first step where your reasoning differed from the explanation. Turn that step into a question, answer it without looking, then change one condition in the example and explain what would change. A correct guess is a reason to revisit the method.

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Related lessons

• Exponent rules practice
• Logarithm practice problems
• Right-triangle trigonometry practice

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