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Linear functions practice

Mixed linear equation skills worksheets

Connect graphs, equations and line properties in ten tasks: four graph-to-slope questions, four equation-to-slope questions and two write-and-graph problems.

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Find the slopes in questions 1–8. In questions 9–10, use the supplied slope and y-intercept to write an equation and draw its graph.

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A4

Student worksheetWorksheet with answers
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Keep the three task groups connected

Questions 1–4 find slopes from graphs. Questions 5–8 find slopes from equations. Questions 9–10 use a given slope and y-intercept to write an equation and graph it. This sequence checks whether the learner can move between representations.

Choose a focused mode when options are available. The settings change what the learner is given and what they must produce; the student preview and downloadable PDF use the same questions.

Learning objective

What this activity builds

Move between line representations without confusing a slope, an intercept and an equation.

Worked example

A line has slope −1/2 and y-intercept 1. Write and graph its equation.

y = −(1/2)x + 1, through (0, 1) and (2, 0).

The slope is the coefficient of x and the intercept is the constant. Moving two units right and one down connects the two points on this line.

Teaching notes

Make the practice count

  • Ask which representation is given before calculating.
  • Keep the graph and equation meanings of slope connected.
  • Use the final two tasks to check transfer between representations.
  • Review a focused prerequisite if only one task group causes difficulty.

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Choose your options, update the preview, then download the exact same pages.

Every coordinate grid uses the fixed −5 to 5 unit window. Graph-only modes omit computed response fields; answer editions complete every requested line or solution region.

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2 student pages
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Math SheetNameScore/ 10TeacherDateWorking with Linear EquationsComplete each graph, equation, and property task.1.-5-5-4-4-3-3-2-2-1-11122334455Slope:2.-5-5-4-4-3-3-2-2-1-11122334455Slope:3.-5-5-4-4-3-3-2-2-1-11122334455Slope:4.-5-5-4-4-3-3-2-2-1-11122334455Slope:5.y=2x+3Slope:6.y=-2x+1Slope:7.y=52x-3Slope:8.y=-12x-1Slope:math-sheet.comPage 1 / 2
Math SheetNameScore/ 10TeacherDateWorking with Linear EquationsComplete each graph, equation, and property task.9.Slope:6y-intercept:-4-5-5-4-4-3-3-2-2-1-11122334455Equation:10.Slope:-2y-intercept:-2-5-5-4-4-3-3-2-2-1-11122334455Equation:math-sheet.comPage 2 / 2

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