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.
- Year 10
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.
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.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.What is the step on the $$y$$ axis of this graph?
Q2.A jug of drink is made from 6 cups of juice and 18 cups of soda. Use the ratio table to work out the amount of soda needed for 1 cup of juice.
Q3.What is the missing value in this ratio table?
Q4.A table of values is shown for the relationship $$y = 12 - 4x$$. Which of these is true for this relationship?
Q5.Match each keyword to its definition.
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
Q6.Match each equation of a line to its key features.
$$y = 3x − 2$$ - 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)
Assessment exit quiz
6 Questions
Q1.Which of these descriptions best describes the gradient?
Q2.The gradient of this line is .
Q3.The gradient of this line is .
Q4.The gradient of this line is .
Q5.What is the equation of this line?
Q6.Match each line to its correct equation.
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) - $$y={2\over 3}x - 2$$
