JENECONKMaths Universe

Linear Graphs

Ages 12–15

Difficulty adapts to you

Linear Graphs

A linear graph shows a constant rate of change. In y = mx + c, m is the gradient and c is where the line crosses the y-axis.

Your goals

  • ✓You can create and interpret straight-line graphs.
  • ✓You can use gradient, y-intercept correctly.
  • ✓You can substitute a point into the equation.

Words to know

gradient:
The change in y for each one-unit increase in x.
y-intercept:
The y-value where a graph crosses the y-axis.

Examples

  • 1For y = 2x + 1, when x = 3, y = 7.
  • 2A gradient of 4 means y increases by 4 whenever x increases by 1.

More than one way to solve it

Try each method, then choose the one you can explain and check most clearly.

Method 1

Table of values

Best for: Plotting a reliable straight line
  1. 1.Choose several x-values.
  2. 2.Substitute each into the equation.
  3. 3.Plot the points and join with a straight line.

Example: For y = 2x + 1, x = 0, 1, 2 gives y = 1, 3, 5.

Method 2

Gradient and intercept

Best for: Quick graph sketching
  1. 1.Plot the y-intercept.
  2. 2.Use rise over run for the gradient.
  3. 3.Repeat the step and draw the line.

Example: For y = 3x - 2, start at -2 and move up 3 for every 1 right.

Check these

  • • Do not swap the gradient and y-intercept in y = mx + c.
  • • Keep every number, symbol, label, and unit in its correct place.
  • • Choose the method that makes each step easiest to explain and check.

Helpful habits

  • • Read the whole question before choosing what to do.
  • • Show one clear step at a time and check each step.
  • • If you are stuck, draw a model, try smaller numbers, or revisit the example.

Now try your own

Create your own linear graphs example, solve it, and explain how you checked it.

Professor Wise Owl

Professor Wise Owl

Wisdom & Understanding

“Every expert was once a beginner. You are on your way!”