Skip to content
Auralith Learning

Year 8 · Maths · Coordinates and straight lines · Lesson 3

Gradient and y = mx + c

Learn what the gradient of a line means, find it from a graph by counting squares, find the y-intercept, and use y = mx + c to read, write and draw straight lines, including parallel lines.

Whiteboard video lesson: Gradient and y = mx + c

31-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Understand gradient as steepness
  • Find the gradient of a line from a graph
  • Find the y-intercept of a line
  • Use y = mx + c to identify gradient and intercept
  • Recognise parallel lines and draw lines from their equations

The method

  1. In y = mx + c, m is the gradient and c is the y-intercept.
  2. Gradient = how far up for every 1 across.
  3. Uphill is positive, downhill is negative.
  4. Parallel lines have the same gradient.

Key words: gradient, y-intercept, y = mx + c, parallel, steepness.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

Write down the gradient and y-intercept of y = 2x + 7.

  1. Step 1: Compare with y = mx + c
  2. Step 2: m = 2 (the number in front of x)
  3. Step 3: c = 7 (the number on its own)

Answer: gradient 2, y-intercept 7

Question 2

Write down the gradient and y-intercept of y = 5x − 2.

  1. Step 1: Compare with y = mx + c
  2. Step 2: m = 5 (the number in front of x)
  3. Step 3: c = −2 (the number on its own)

Answer: gradient 5, y-intercept −2

Question 3

Write down the gradient and y-intercept of y = −x + 4.

  1. Step 1: Compare with y = mx + c
  2. Step 2: m = −1 (the number in front of x)
  3. Step 3: c = 4 (the number on its own)

Answer: gradient −1, y-intercept 4