# 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.

## 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

### 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.

### 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.

### 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

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) -

$$y={2\over 3}x - 2$$