# Parallel linear graphs

I can identify, from their equations or graphs, whether two lines are parallel.

# Parallel linear graphs

I can identify, from their equations or graphs, whether two lines are parallel.

## Lesson details

### Key learning points

- Two lines are parallel if they are equidistant and never touch.
- For linear graphs, the rate of change is constant.
- If the gradients are the same then the linear graphs may be parallel.
- The y-intercepts must be different, otherwise the lines are the same.

### Common misconception

Lines are parallel if they have the same gradient.

Lines are parallel if they have the same gradient and different y-intercepts. Two lines are parallel if they are straight lines that are always the same non-zero distance apart.

### 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.

Parallel - Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.

### 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

$$y = 5x + 6$$ -

gradient is 5

$$y = 6x + 3$$ -

gradient is 6

$$y = 3 - 5x$$ -

gradient is -5

$$y = -(6 + 3x)$$ -

gradient is -3

$$y + 6x = 5$$ -

gradient is -6

$$2y = 6x + 5$$ -

gradient is 3

## Exit quiz

### 6 Questions

$$y = x + 4$$ -

$$y = x + 100$$

$$ y = 2x - 3$$ -

$$ y = 2x + 0.5$$

$$ y = 3 - x $$ -

$$ y = -x + {5\over 2}$$

$$ y = 3x - 1$$ -

$$ y = 4 + 3x$$

$$ y = -2x + 1$$ -

$$ y = 3 - 2x$$