New
New
Year 8

The intercept point

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

New
New
Year 8

The intercept point

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

Lesson details

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.

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.

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.

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
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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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)