Checking and securing understanding of finding the equation of the line from the graph
I can find the equation of the line from the graph.
Checking and securing understanding of finding the equation of the line from the graph
I can find the equation of the line from the graph.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- Linear equations can be rearranged into the form y = mx + c
- The gradient (m) and the y-intercept (c) can be determined from the graph.
- The amount y changes when x increases by one is the rate of change and called the gradient.
- Where the graph crosses the y-axis is the value of the y-intercept.
- The equation of the line can be written in the form y = mx + c
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 the graph, 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 the graph, 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.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
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
Starter quiz
6 Questions




constant -
a term that does not vary
coefficient -
the multiplier of a specified variable in a term
gradient -
a measure of how steep a line is
intercept -
the point where a line crosses a specified axis
origin -
the point with coordinates (0, 0)
equation of a straight line -
a relationship which, when plotted, forms a straight line
$$y = 3x − 2$$ -
gradient 3, $$y$$-intercept (0, -2)
$$y = 3x + 2$$ -
gradient 3, $$y$$-intercept (0, 2)
$$y = 2 - 3x$$ -
gradient -3, $$y$$-intercept (0, 2)
$$y = 2x - 3$$ -
gradient 2, $$y$$-intercept (0, -3)
$$y = 3 + 2x$$ -
gradient 2, $$y$$-intercept (0, 3)
$$y = 3 - 2x$$ -
gradient -2, $$y$$-intercept (0, 3)
Exit quiz
6 Questions





A (blue) -
$$y=-{2\over 3}x - 2$$
B (pink) -
$$y=-{3\over 2}x - 2$$
C (black) -
$$y={3\over 2}x $$
D (green) -
$$y={3\over 2}x - 2$$
E (purple) -
$$y={2\over 3}x - 2$$