Checking and securing understanding of finding the equation of the line from coordinates
I can find the equation of the line from two coordinate pairs as well as from the gradient and one coordinate pair.
Checking and securing understanding of finding the equation of the line from coordinates
I can find the equation of the line from two coordinate pairs as well as from the gradient and one coordinate pair.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- The gradient can be found from two points by considering the change in y over the change in x
- The y-intercept can be found using the gradient and one of the points.
- By substituting the gradient and one coordinate pair into the general equation, you can find the y-intercept.
- The y-intercept occurs when the x value is zero.
- 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. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction.
Intercept - An intercept is the coordinate where a line or curve meets a given axis.
Common misconception
Writing equations of the form y = mx + c and getting the gradient and y-intercept the wrong way round.
Graphing software can be used to show that adding a constant is a translation of the graph. Remind pupils that the y-intercept is when x is zero which is why it is the constant in the equation. They can substitute x = 0 to check.
To help you plan your year 10 maths lesson on: Checking and securing understanding of finding the equation of the line from coordinates, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Checking and securing understanding of finding the equation of the line from coordinates, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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The assessment exit quiz will test your pupils' understanding of the key learning points.
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Explore more key stage 4 maths lessons from the Linear graphs unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Starter quiz
6 Questions
$$y = 5x + 5$$ -
gradient $$5$$ and $$y$$-intercept $$(0, 5)$$
$$y = 10 - 5x$$ -
gradient $$-5$$ and $$y$$-intercept $$(0, 10)$$
$$2y + 5x = 10$$ -
gradient $$-{5\over 2}$$ and $$y$$-intercept $$(0, 5)$$
$$10y + 4x = 10$$ -
gradient $$-{2\over 5}$$ and $$y$$-intercept $$(0, 1)$$
$$5y = 2x + 5$$ -
gradient $${2\over 5}$$ and $$y$$-intercept $$(0, 1)$$
$$y - {5\over 2}x = 5$$ -
gradient $${5\over 2}$$ and $$y$$-intercept $$(0, 5)$$
Exit quiz
6 Questions
(5, 4) and (6, 8) -
$$y = 4x - 16$$
(5, 4) and (7, 1) -
$$2y + 3x = 23 $$
(5, 4) and (8, 13) -
$$y - 3x = -11 $$
(-5, 4) and (-3, 7) -
$$2y - 3x = 23 $$
(-5, 4) and (-6, 3) -
$$y - x = 9 $$