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Lesson details

Learning outcome

I can calculate the intercept point from a graph and from two coordinate pairs.

Key learning points

  1. The y-intercept can be found by considering the graph.
  2. The y-intercept occurs when the x value is zero.
  3. The gradient can be found from two points.
  4. The y-intercept can be found using the gradient and one of the points.
  5. It is useful to check using the second point while understanding the limitations of this check.

Keywords

  • Gradient - The gradient is a measure of how steep a line is.

  • Intercept - An intercept is the coordinate where a line or curve meets a given axis.

  • Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

Common misconception

Writing the y intercept as a single value or getting the x and y coordinates the wrong way around.

Encourage writing the y intercept as a coordinate. Stating 'lines cross the y axis when x=0' can help pupils write the coordinate correctly.

Teacher tip

A good opportunity here to link to work on linear sequences. Finding the y intercept from 2 coordinates is the same skill as finding the initial term in a linear sequence. Make it clear that the first term is when n=1 but the y intercept is when x=0

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
except where otherwise stated. See Oak's terms & conditions
(Collection 2).

Lesson video

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Prior knowledge starter quiz

6 Questions

Q1.
Which of these sequences are linear?

Correct answer: $$3n + 1$$
Correct answer: $$7 - 5n$$
$$n^2$$
$$5n^3 - 15$$
Correct answer: $$2n - 5$$

Q2.
Which of these best describes an intercept point?

A point on the line where the $$x$$ and $$y$$ coordinates are the same
A point on the line which you use to find the gradient.
A point on the line where both values are positive.
Correct answer: A point on the line where it meets an axis.

Q3.
The tables shown have been labeled A,B,C,D,E. Match the table with the correct gradient.

An image in a quiz
Correct Answer:A,2

2

Correct Answer:B,-2

-2

Correct Answer:C,-4

-4

Correct Answer:D,5

5

Correct Answer:E,4

4

Q4.
In a linear sequence the common difference is 3 and the tenth term is 32. What is the first term?

An image in a quiz
Correct Answer: 5, five

Q5.
What is the gradient of the line which passes through the coordinates (4, 7) and (6,11) ?

Correct Answer: 2, two

Q6.
What is the gradient of the line which passes through the coordinates (2, -6) and (0,-1) ?

$$-3$$
Correct answer: $$-{5\over 2}$$
$$-{2\over 5}$$
$$2\over 5$$
$$5\over 2$$

6 Questions

Q1.
What is the $$y$$-intercept for the line formed when this table of values is plotted?

An image in a quiz
(0,2)
(2,0)
Correct answer: (0,6)
(6,0)
(-2,12)

Q2.
Which of these coordinates could be a $$y$$-intercept?

Correct answer: (0,0)
(3,0)
Correct answer: (0,-7)
(0.2,0)
Correct answer: (0,$$2\over5$$)

Q3.
The graph shows 5 lines labelled A, B, C, D, E. Match the line to its corresponding $$y$$ intercept.

An image in a quiz
Correct Answer:A (purple),(0,0)

(0,0)

Correct Answer:B (pink),(0,3)

(0,3)

Correct Answer:C (green),(0,-1)

(0,-1)

Correct Answer:D (blue),(0,-3)

(0,-3)

Correct Answer:E (black),(0,4)

(0,4)

Q4.
What is the $$y$$ intercept for the line belonging to this table of values?

An image in a quiz
(0,9)
(0,1)
(0,0)
(0,-3)
Correct answer: (0,-7)

Q5.
What is the $$y$$ intercept for the line belonging to this table of values?

An image in a quiz
Correct answer: (0,26)
(0,24)
(0,13)
(0,8)
(0,-14)

Q6.
Match up the $$y$$-intercepts with the corresponding lines.

Correct Answer:(0,-3),The line through (4,5) and (5,7)

The line through (4,5) and (5,7)

Correct Answer:(0,0),The line through (1,3) and (3,9)

The line through (1,3) and (3,9)

Correct Answer:(0,15),The line through (10,5) and (13,2)

The line through (10,5) and (13,2)

Correct Answer:(0,-15),The line through (4,-3) and (8,9)

The line through (4,-3) and (8,9)


To help you plan your 8 maths lesson on: The intercept point, download all teaching resources for free and adapt to suit your pupils' needs...