Mathematics (Core)Exam code: 0580

Linear Graphs

Coordinate Geometry and Graphs

PractiseFlashcards

From an equation

  • Build a small table of values by substituting three x values that are spread across the axes you are given
  • Three points, not two: a slip in one of three points shows up because it misses the line through the other two, whereas two points always look convincing
  • Plot the points and join them with a ruled line that runs the full width of the grid
Two straight lines drawn on the same grid: a steep uphill line through (0, −1) and (1, 2), stepping 1 across and 3 up, and a shallow downhill line through (0, 3) and (5, 0)
Source: Drawing linear graphs by Save My Exams
  • Alternatively start at (0, c) and step out the gradient, going one right and m up each time, down instead if m is negative
  • For a gradient written as a fraction, step across by the bottom number and up by the top number
A shallow uphill line on a grid through (0, −1) and (3, 1), with a dashed triangle showing 3 across against 2 up, giving a gradient of two thirds
Source: Gradient of a line by Save My Exams

Worked example

Drawing a line from its equation

Draw y = 2x + 3 for x from −1 to 2.

Solution:

  • Build a short table of values
  • x = −1 gives y = 1; x = 0 gives 3; x = 1 gives 5; x = 2 gives 7
  • Plot (−1, 1), (0, 3), (1, 5) and (2, 7), and join them with a ruled line
A grid from x = −1 to 3 and y = −2 to 8 with y = 2x + 3 ruled through the crosses at (−1, 1), (0, 3), (1, 5) and (2, 7)

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