## Algebra x and y intercepts

**Introduction :**

In algebra, intercept means a point at which a line, curve, or surface intersects an axis. Intercept is classified into two types as follows.

- X intercept
- Y intercept

**X intercept:**

- In algebra, the x-intercept of a line is a point at which the line cuts the X-axis.
- The x-intercept of a line is denoted as ( x, 0 )

**Y intercept:**

- In algebra, the y-intercept of a line is a point at which the line cuts the Y-axis.
- The y-intercept of a line is denoted as ( 0, y )

**Algebra x and y intercepts - Example problem 1:**

**Find x and y intercept of the line equation 3x + y = 7.**

**Solution:**

**Step 1: Given equation**

**3x + y = 7**

**Step 2: Find x intercept**

To finding x intercept, plug y = 0 in the given equation 3x + y = 7 and solve for x

**3x + y = 7**

**Plug y = 0,**

**3x + 0 = 7**

3x = 7

Divide by 3 on both sides,

x = `7/3`

Therefore, the x intercept of the given equation is (`7/3` , 0)

Step 3: Find y intercept

**To find y intercept, plug x = 0 in the given equation 3x + y = 7 and solve for y**

3x + y = 7

Plug x = 0,

3(0) + y = 7

y = 7

Therefore, the x intercept of the given equation is (0, 7)

Step 4: Solution

**X intercept = (`7/3` , 0)**

**Y intercept = (0, 7)**

Algebra x and y intercepts - Example problem 2:

**Find x and y intercept of the line equation y = 2x - 13**

**Solution:**

**Step 1: Given equation**

**y = 2x - 13**

**Step 2: Find x intercept**

To find x intercept, plug y = 0 in the given equation y = 2x - 13 and solve for x

**y = 2x - 13**

**Plug y = 0,**

**0 = 2x - 13**

Add 13 on both sides of the equation,

13 = 2x

Divide by 2 on both sides,

`13/2` = x

x = 6.5

Therefore, the x intercept of the given equation is (6.5, 0)

Step 3: Find y intercept

**To find y intercept, plug x = 0 in the given equation y = 2x - 13 and solve for y**

y = 2x - 13

Plug x = 0,

y = 2(0) - 13

y = - 13

Therefore, the x intercept of the given equation is (0, - 13)

Step 4: Solution

**X intercept = (6.5, 0)**

**Y intercept = (0, - 13)**