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# How can you work out where a graph crosses the x axis or y axis.

To find out where a graph crosses the y - axis all you need to do is substitute x = 0 into the equation and find the value of the y coordinate.

To find out where a graph crosses the x – axis all you need to do is substitute y = 0 into the equation and find the value of the x coordinate.

**Example 1**

Find out the points where the graph 3x – 2y = 12 crosses the x and y axis.

First find out where the graph crosses the y axis. Do this by subbing in x = 0 and solving the resulting equation:

3x – 2y = 12

3 × 0 – 2y = 12

-2y = 12

y = 12/-2

y = -6

So the graph crosses the y axis at (0,-6)

Next find out where the graph crosses the x axis. Do this by subbing in y = 0 and solving the resulting equation:

3x – 2y = 12

3x – 2 × 0 = 12

3x = 12

x = 12/3

x = 4

So the graph crosses the x axis at (4,0)

By drawing the graph of 3x – 2y = 12 you can see that these two values are correct.

**Example 2**

Find out the points where the graph y = x² - 3x - 10 crosses the x and y axis.

First find out where the graph crosses the y axis. Do this by subbing in x = 0 and solving the resulting equation:

y = x² - 3x - 10

y = 0² - 3 × 0 – 10

y = -10

So the graph crosses the y axis at (0,-10)

Next find out where the graph crosses the x axis. Do this by subbing in y = 0 and solving the resulting equation:

y = x² - 3x - 10

0 = x² - 3x - 10

This is a quadratic equation so you need to factorise this equation in order to solve it:

0 = (x-5)(x+2)

So either x – 5 = 0 or x + 2 = 0

So x = 5 or x = -2

So the graph crosses the x axis at (5,0) and (-2,0)

By drawing the graph of y = x² - 3x - 10 you can see that these values are correct.

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