Skip to main content
MathidiaMathematics Academy
Coordinates, graphs and transformations
Lesson 68 of 75
Standard practice

Straight-line graphs

Objective. Generate and plot points from simple linear rules.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

A straight-line graph is produced by plotting points that satisfy a linear rule connecting x and y, such as y=2x+1. To generate points, substitute several values of x into the rule and calculate the corresponding y values, then plot each pair as a coordinate. For example, substituting x=0,1,2 into y=2x+1 gives the points (0,1), (1,3) and (2,5). Joining these plotted points with a ruler produces a straight line representing every solution to the rule, including values between the plotted points.

Worked example

Generate the coordinates needed to plot the straight-line graph of y = 3x − 2 for x = 0, 1 and 2.

3 … 2
Coordinate grid with the line 3 … 2
  1. 1Substitute x=0: y=3×0−2=−2, giving (0,−2).
  2. 2Substitute x=1: y=3×1−2=1, giving (1,1).
  3. 3Substitute x=2: y=3×2−2=4, giving (2,4).
  4. 4List the three coordinate pairs needed to plot the line.

Answer: (0,−2), (1,1), (2,4)

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Pupils sometimes plot points in the wrong order, swapping x and y values when reading them from a table. Always check the table heading matches each coordinate before plotting.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard