## Key points

Graphs of two or more straight lines can be used to solve simultaneous linear equations.

The graph of a straight line can be described using an .

- lines are written as \(y = c\)
- lines are written as \(x = c\)
- are written as \(y = mx + c\)

\(m\) is a number which is a measure of the steepness of the line. This is the .

\(c\) is the number where the line crosses the \(y\)-axis. This is the \(y\).

The of the points on an oblique line are calculated by given values of \(x\) into the equation \(y = mx + c\)

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## Recognise and draw the lines ๐ = ๐ and ๐ = -๐

All the points on the line \(y = x\) have coordinates with equal values for \(x\) and \(y\)

- To draw the line \(y = x\):
- Plot points with coordinates where \(x\) and \(y\) are equal. Three points are sufficient, but more can be plotted.
- Draw a line through the plotted points.

All the points on the line \(y = -x\) have coordinates with values for \(x\) and \(y\) that are equal in but with opposite signs.

If \(x\) is positive, \(y\) is negative. If \(x\) is negative, \(y\) is positive.

- To draw the line \(y = -x\):
- Plot points with coordinates where \(x\) and \(y\) have equal magnitude but opposite signs.
- Draw a line through the plotted points.

### Examples

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### Question

One graph shows \(y = x\) and one shows \(y = -x\). Which graph shows \(y = x\)?

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## Draw the graph ๐ = ๐๐ + ๐ by creating a table of values

\(m\) is a number which measures the steepness of the line. This is known as the **gradient**.

\(c\) is the number where the line crosses the \(y\)-axis. This is the \(y\)**-intercept**.

- To draw a graph of \(y = mx + c\) for given values of \(x\):
- Use the given values for \(x\) to draw a table of values for \(x\) and \(y\)
- each value of \(x\) into the equation to find the valueof \(y\). Each pair of values give a coordinate.
- Use the coordinates to decide on that will take all the values of \(x\) and \(y\)
- Plot the coordinates and draw a line through the points. Label the line with the equation.

### Example

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### Questions

Question 1: Complete the table of values for \(y = 3x + 8\) for values of \(x\) from -2 to 2

**A table of values can also be used to find the coordinates of a line with a negative gradient.**

Question 2: Complete the table of values for \(y = 3 โ 2x\) for values of \(x\) from -1 to 3

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## Reading ๐ and ๐ coordinates from a graph

A position on a graph is defined by coordinates (\(x\), \(y\)). When one coordinate is given, the second can be read from the graph.

To find a \(y\)-coordinate from a given \(x\)-coordinate:

- On the \(x\)-axis, locate the given amount.
- Draw a vertical line, using a ruler, from the given amount up to the line.
- Draw a horizontal line, using a ruler, from the line across to the \(y\)-axis.
- Read the value on the \(y\)-axis.

To find an \(x\)-coordinate from a given \(y\)-coordinate:

- On the \(y\)-axis, locate the given amount.
- Draw a horizontal line, using a ruler, from the given amount across to the line.
- Draw a vertical line, using a ruler, from the line down to the \(x\)-axis.
- Read the value on the \(x\)-axis.

### Examples

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### Question

Use the graph to find the value of \(x\) when \(y = 3\)

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## Practise reading and plotting linear equation graphs

### Quiz

Practise reading and plotting linear equation graphs with this quiz. You may need a pen and paper to help you.

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## Real-life maths

Linear graphs are commonly used when converting between different units of measurement.

For example, swapping between temperatures in degrees Celsius (ยฐC) and degrees Fahrenheit (ยฐF), exchanging between different currencies, such as pounds and euros, or changing inches into centimetres.

Linear graphs are useful to pharmacists and scientists in the pharmaceutical industry when working out the correct strength of drugs.

The amount of a drug for a given volume of medicine is critical, both for the medicine to be effective and for the safety of the patient.

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### Game - Divided Islands

Play the Divided Islands game! gamePlay the Divided Islands game!

Using your maths skills, help to build bridges and bring light back to the islands in this free game from BBC Bitesize.

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