**Introduction :**

Interceptis a point where the equation cuts either x axis or y - axis. The pointat which the equation cuts the x axis is called as x -intercept and thepoint at which the equation cuts the y axis is called as y -intercept. The equation can cut the x axis or y axis more than once. So, we can have 0 or more intercepts for a given equation. The x intercepts are of the form (x,0) because they lie on x axis and y intercepts are of the form (0,y) because they lie on y axis.

| number and type of x intercept | number and type of y intercept |

Figure 1 | 1 (positive) | 1( positive) |

Figure 2
| 1 (negative) | 1 (negative) |

Figure 3
| 1 (negative) | 1 (positive) |

Figure 4
| 1 (positive) | 1 (negative) |

Figure 5
| 1 (negative) | 0 |

Figure 6
| 0 | 1 (positive) |

Figure 7
| 1 (negative) | 2 (positive and negative) |

Figure 8
| 2 (negative and positive) | 1 (positive) |

## How to find intercept:

Step1: We need to find x intercept and y intercept.

Step 2: Put x="0" in the given equation to get y intercept.

Step 3: Put y="0" in the given equation to get x intercept.

## Example problem:

What is intercept for the equation 5x + 9y = 45

**Solution: **For x intercept put y="0" in the given equation

5x + 9 (0) = 45

5x = 45

x = $\frac{45}{5}$

x = 9

x intercept is (9,0)

For y intercept put x="0" in the given equation

5(0)+9y=45

9y = 45

y = $\frac{45}{9}$

y = 5

y intercept is(0,5)

## Practice problems:

Problem 1: What is intercept(s) for the given equation 4x+6y=8

Problem 2: What is intercept(s) for the given equation x+y=0

Problem 3: What is intercept for the given equation 6y="8

Problem 4: What is intercept for the given equation 5x="9

Answers:

1) (2, 0) and (0, 4/3)

2) 0 and 0

3) 0 and (0, 4/3)

4) (9/5, 0) and 0

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