Coordinate Geometry • Topic 3 of 3

Graphing Simple Relations

What is Graphing a Relation? A relation is a set of ordered pairs. Graphing a relation means plotting all points that satisfy a given condition or equation.

Common Relations to Graph:

RelationDescriptionExample
\(x = k\)Vertical line at \(x = k\)\(x = 3\) (vertical line)
\(y = k\)Horizontal line at \(y = k\)\(y = 2\) (horizontal line)
\(y = x\)Diagonal line (slope 1)Points like (0,0), (1,1), (2,2)
\(y = mx + c\)Straight line\(y = 2x + 1\)
\(x = y\)Line at 45°Points where coordinates are equal

How to Graph a Simple Equation:

  • Make a table of values (choose 3-5 x-values)
  • Calculate corresponding y-values
  • Plot each ordered pair
  • Connect the points (if they form a line)

Identifying Patterns:

  • Linear relations (\(y = mx + c\)) form straight lines
  • The line \(y = x\) passes through origin at 45°
  • Vertical lines: \(x = \text{constant}\) (all points share same x)
  • Horizontal lines: \(y = \text{constant}\) (all points share same y)
Graphing Linear Relationsxy-5-5-4-4-3-3-2-2-1-111223344550y=xy=2xy = xy = 2xSlope=gradient
Solved Examples
1
Worked Example
Make a table of values for \(y = x + 2\) for \(x = 0, 1, 2, 3\).
Solution- \(x = 0\) → \(y = 0 + 2 = 2\) → \((0, 2)\) - \(x = 1\) → \(y = 1 + 2 = 3\) → \((1, 3)\) - \(x = 2\) → \(y = 2 + 2 = 4\) → \((2, 4)\) - \(x = 3\) → \(y = 3 + 2 = 5\) → \((3, 5)\) - **Answer: | x | y | |---|---| | 0 | 2 | | 1 | 3 | | 2 | 4 | | 3 | 5 | *Example 2: Plot the graph of \(y = 2x\) for \(x = -2, -1, 0, 1, 2\). Solution: - \(x = -2\) → \(y = -4\) → \((-2, -4)\) - \(x = -1\) → \(y = -2\) → \((-1, -2)\) - \(x = 0\) → \(y = 0\) → \((0, 0)\) - \(x = 1\) → \(y = 2\) → \((1, 2)\) - \(x = 2\) → \(y = 4\) → \((2, 4)\) - Plot all points and draw a straight line through them - **Answer:** A straight line passing through origin with slope 2 *Example 3: Write the equation for a horizontal line that passes through the point \((3, 5)\). Solution: - Horizontal line has constant y-value - The point \((3, 5)\) has \(y = 5\) - Every point on this line has \(y = 5\) - Equation: \(y = 5\) - **Answer:** \(y = 5\)

Key Points

  • To graph a relation, plot points that satisfy the condition
  • \(y = mx + c\) represents a straight line (m = slope, c = y-intercept)
  • \(x = \text{constant}\) → vertical line
  • \(y = \text{constant}\) → horizontal line
  • \(y = x\) is a diagonal line through origin (45° angle)
  • Use a table of values to find points before plotting
  • ---
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.The graph of $y=x$ passes through the:
Explanation: Through $(0,0)$.
Q2.The graph of $y=3$ is a:
Explanation: Horizontal.
Q3.The graph of $x=2$ is a:
Explanation: Vertical.
Q4.A linear relation graphs as a:
Explanation: Straight line.
Practice more MCQs → 📝 Assignment · 35 marks