New
New
Year 8

Rate of change from a coordinate pair

I can calculate the rate of change (gradient) from two coordinate pairs.

New
New
Year 8

Rate of change from a coordinate pair

I can calculate the rate of change (gradient) from two coordinate pairs.

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Lesson details

Key learning points

  1. Two coordinate pairs can be plotted and joined with a line.
  2. The gradient of this line can be calculated.
  3. The gradient between two points can be calculated without drawing the line.
  4. The gradient between two points can be calculated without drawing the points.
  5. The gradient between any two points on a straight line is the gradient of the line.

Keywords

  • Parallel - Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.

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

Common misconception

When calculating gradient from coordinates, pupils get positive and negative gradients mixed up.

Encourage pupils to sketch the coordinates first and then always look at a positive increase in x.

In the first learning cycle, pupils can investigate how changing the scale can change the gradient of a line which moves right 1 square up one square. They could think of other scales for the axes and see what the gradient would become.
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).

Lesson video

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6 Questions

Q1.
What is the missing number in this ratio table?
An image in a quiz
$$1\over 7$$
$$1\over 5$$
$$5\over 7$$
Correct answer: $$7\over 5$$
Q2.
What is the gradient of this line?
An image in a quiz
Correct Answer: 2, two
Q3.
What is the gradient of this line?
An image in a quiz
Correct answer: -6
-3
3
4
6
Q4.
Match the points on the graph below with their corresponding coordinates.
An image in a quiz
Correct Answer:A,(3,4)

(3,4)

Correct Answer:B,(6,5)

(6,5)

Correct Answer:C,(6,1)

(6,1)

Correct Answer:D,(-2,1)

(-2,1)

Correct Answer:E,(-5,3)

(-5,3)

Correct Answer:F,(-1,2)

(-1,2)

Q5.
Match the directed number calculations with the correct answer.
Correct Answer:$$11 - (-30)$$,41

41

Correct Answer:$$-11 - 30$$,-41

-41

Correct Answer:$$ 11 + (-30)$$,-19

-19

Correct Answer:$$ -11 - (-30)$$,19

19

Q6.
Which is the correct ratio table for the graph shown?
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz

6 Questions

Q1.
Work out the gradient of the line which passes through (6,20) and (7,25).
An image in a quiz
Correct Answer: 5
Q2.
Calculate the gradient of this line which goes through the origin.
An image in a quiz
Correct Answer: 7, seven
Q3.
A line with negative gradient is drawn through ( -4, 5) and one of these coordinates. Which coordinate could it be?
(-8,2)
(-2,7)
Correct answer: (-1,3)
(2,8)
Q4.
Work out the gradient of the line joining the coordinates (-5,11) and (-2,2).
An image in a quiz
$$-{1\over 3}$$
$$-{9\over 7}$$
Correct answer: $$ -3$$
$$-{11\over 3}$$
$$-{11\over 2}$$
Q5.
Match the two coordinate pairs to the gradient of the line passing through them.
Correct Answer:(5,6) and (6,8),$$2$$

$$2$$

Correct Answer:(5,6) and (8, 15),$$3$$

$$3$$

Correct Answer:(5,6) and (-3,2),$$1\over 2$$

$$1\over 2$$

Correct Answer:(5,6) and (7,3) ,$$-{3\over 2}$$

$$-{3\over 2}$$

Correct Answer:(5,6) and (-4, 15),$$-1$$

$$-1$$

Q6.
Which set of 3 coordinates lie on a straight line?
Correct answer: (-2,-1), (0,7) and (1,11)
(-5,-3), (-3,3) and (2,13)
Correct answer: (1,12), (5,10) and (7,9)