Negative rate of change from a graph | Maths | Quizalize & Oak National Academy

Starter quiz

Which of these is the correct explanation for how gradient is calculated?

rate of change in $x$ direction with respect to positive $y$ direction

rate of change in $x$ direction with respect to negative $y$ direction

rate of change in $y$ direction with respect to negative $x$ direction

rate of change in $y$ direction with respect to positive $x$ direction ✓
The gradients of all 4 lines are ______.

equal

even

negative

positive ✓

straight
What is the gradient of this line?

'4' ✓
What is the gradient of this line?

'6' ✓
Which of these tables of values show a relationship which will have a positive gradient when plotted?

A ✓

B

C ✓

D

E ✓
Which is the correct ratio table for this graph?

Which of these graphs have a negative gradient?

A (purple) ✓

B (blue) ✓

C (pink)

D (green) ✓
Match the graphs to the correct gradient.

A (purple)

⇔

3 ✓

B (black)

⇔

2 ✓

C (pink)

⇔

1 ✓

D (blue)

⇔

-1 ✓

E (green)

⇔

-2 ✓
What is the gradient of this line?

'-3' ✓
What is the gradient of this line?

$-{3\over 2}$

$-{2\over 3}$ ✓

$-{1\over 2}$

$2\over 3$

$3\over 2$
Starting with the steepest, put these gradients in order of steepness.

1

⇔

$-8$

2

⇔

$6$

3

⇔

$5\over 2$

4

⇔

$-1$

5

⇔

$-{2\over 3}$

6

⇔

$1\over 2$
Which lines would be parallel to the one shown if drawn on the same axes?

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Graphs can be described by looking at how quickly they fall.
The amount y decreases when x increases by one is the rate of change and is called the gradient.
The gradient will be negative if y decreases as the graph moves to the right.
The gradient can be found from any linear graph.
The gradient tells us important information about the relationship.

Pupils may think lines with gradients 2 and -2 are parallel.

Lines have to have the exact same gradient to be parallel. A line with a negative gradient will intersect a line with a positive gradient .

Gradient - The gradient is a measure of how steep a line is.
Absolute value - The absolute value of a number is its distance from zero.
Parallel - Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.