The equation of a line from its graph

The Maths Habit
Walkthrough to print

Work out the gradient

  1. A line goes across 2, up 10.

    5

  2. A line goes across 4, down 2.

    −12

  3. A line goes through (1, 2) and (3, 8).

    3

Which is the odd one out? Why?

y = 2x + 1     y = 2x − 3

y = 5x + 1     y = 2x

y = 5x + 1: the others all have 2x

y = 2x: nothing is added or taken away

y = 2x − 3: the only one that takes away

Gradient
How far the line goes up or down for every 1 across.
y intercept
Where the line crosses the y axis.

y = mx + c

What is the gradient?

y = 3x − 1 3

Where does it cross the y axis?

y = 3x − 1 (0, −1)

Write the equation

Gradient 2, crosses the y axis at 5 y = 2x + 5

Write the equation

Gradient −1, crosses the y axis at 4 y = −x + 4

  1. Gradient 4, crosses the y axis at −3. Write the equation.

    y = 4x − 3

  2. What is the gradient of y = 5 − 2x?

    −2

  3. Where does y = 4x + 7 cross the y axis?

    (0, 7)

  4. Gradient −3, crosses the y axis at 1. Write the equation.

    y = −3x + 1

Equation of a line

  1. GradientAcross first, then up or down.
  2. Find cPut m and one point into y = mx + c.
  3. Write the equationPut m and c into y = mx + c.
  4. CheckPut in the other point.
    It works.
m = change in ychange in x
y = mx + c
y value = m × x value + c
point 2 fits the equation ✓
goes down? the gradient is negative
then solve it for c
Walkthrough to print

Find the equation of the line. y = 2x + 1

0123450246810
where it crosses the y axisc =1
gradient: up or down for every 1 acrossm =2

Find the equation of the line. y = x + 2

0123450246810
where it crosses the y axisc =2
gradient: up or down for every 1 acrossm =1

Find the equation of the line. y = 2x + 1

0123450246810
where it crosses the y axisc =1
gradient: up or down for every 1 acrossm =2

Find the equation of the line. y = −2x + 8

0123450246810
where it crosses the y axisc =8
gradient: up or down for every 1 acrossm =−2

Find the equation of the line. y = 2x + 1

0123450246810
where it crosses the y axisc =1
gradient: up or down for every 1 acrossm =2

Find the equation of the line. y = 3x + 1

0123450246810

Find the equation of the line. y = 2x + 1

0123450246810
where it crosses the y axisc =1
gradient: up or down for every 1 acrossm =2

Find the equation of the line. y = −x + 6

0123450246810

Find the equation of the line. y = 2x + 1

0123450246810
where it crosses the y axisc =1
gradient: up or down for every 1 acrossm =2

Find the equation of the line. y = 4x

0123450246810

The equation of a line from its graph worksheet, page 1

Answer sheet

  1. Which is steeper: y = 3x + 1 or y = 2x + 9?

    y = 3x + 1

  2. A line is parallel to y = 2x + 1 and crosses the y axis at −4. Write its equation.

    y = 2x − 4

  1. A line has gradient −4 and crosses the y axis at 3. Write its equation.

    y = −4x + 3

  2. Find the equation of the line.

    y = 2x − 1
    xy−1012−3−2−10123

  3. Ivy says the line y = 6 − 2x has a gradient of 6. Is Ivy right? Explain.

    No: the gradient is −2
Exit tickets to print