Estimating the gradient of a curve
I can estimate the gradient of a curved part of the graph by considering the gradient of a straight line connecting two points.
Estimating the gradient of a curve
I can estimate the gradient of a curved part of the graph by considering the gradient of a straight line connecting two points.
Lesson details
Key learning points
- The gradient of a curve can be estimated.
- You can estimate by drawing a straight line between two points on the graph.
- The closer the points, the more accurate the estimate is.
Common misconception
Pupils may estimate negative gradients incorrectly by drawing gradient triangles the wrong way round or ignoring the fact that the $$y$$ values are decreasing as $$x$$ increases.
Pupils should look at the shape of the graph between two points and decide if it is positive or negative before calculating. If $$y$$ is decreasing as $$x$$ increases then the gradient is negative.
Keywords
Gradient - The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the $$y$$-direction with respect to the positive $$x$$-direction.
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).
Video
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Starter quiz
6 Questions
Exit quiz
6 Questions
$$x=0 \ \text{to} \ x=1$$ -
$$4$$
$$x=1 \ \text{to} \ x=2$$ -
$$-4$$
$$x=2 \ \text{to} \ x=3$$ -
$$-6$$
$$x=3 \ \text{to} \ x=4$$ -
$$-2$$
$$x=4 \ \text{to} \ x=5$$ -
$$7$$