X Intercept Formula | List of X Intercept Formula You Should Know - BYJUS

# X Intercept Formula

The point on the graph of a function where the X-axis intersects is known as the x-intercept. The x-intercept of any curve is the value of the x-intercept at the point where the graph intersects the x-axis or, alternatively, the value of the x-coordinate at the point where the value of the y-coordinate equals zero. In this article, we will study the formula for the x-intercept and solve a few example problems that will give us a better understanding of the formula....Read MoreRead Less

### What is the X-Intercept?

The x-intercept is the location where the line crosses the x-axis of the plane. Thus, the value of the y-coordinate of a linear equation will always be equal to zero whenever it crosses the x-axis. For the x-intercept, the y-coordinate is zero, and for the y-intercept, the x-coordinate is zero. The x-intercept is also known as the horizontal intercept. The equation of a line is given by:

y = mx + c

In general, the horizontal axis is commonly used to represent the variable x and the vertical axis to represent the variable y. Also, m is the slope of the line, and c is the y-intercept of the line.

The equation of a line is also given by:

Ax + By = C.

Here, A, B, and C are constants

### Formula for the X-Intercept

The formula for the x-intercept of the line with the equation Ax + By = C, is,

x = $$\frac{C}{A}$$

The formula for the x-intercept for the line with the equation y = mx + c, is,

x = $$\frac{-C}{m}$$

### Solved Examples

Example 1: Find the x-intercept of the equation, x + 3y = 12.

Solution:

To find the x-intercept, set y = 0 and solve for x.

x + 3 (0) = 12          [substitute zero for y]

x = 12                     [Simplify]

Alternatively,

Comparing the given equation with the equation, Ax + By = C,

A = 1, B = 3 and C = 12

x-intercept = $$\frac{C}{A}~=~\frac{12}{1}~=~12$$

Hence, the x-intercept of the given equation is 12.

Example 2: Find the x-intercept of the equation, 2x + 4y = 8.

Solution:

Comparing the given equation with Ax + By = C,

A = 2, B = 4 and C = 8

x-intercept = $$\frac{C}{A}~=~\frac{8}{2}~=~4$$.

Hence, the x-intercept of the given equation is 4.

Example 3: Find the x-intercept of the equation, y = 2x + 6.

Solution:

Comparing the given equation with y = mx + c ,

m = 2 and c = 6

x-intercept = $$\frac{-c}{m}~=~\frac{-6}{2}~=~-3$$.

Hence, the x-intercept of the given equation is – 3.

Example 4: Rachel is trying to get the equation of a line with a slope of 6 and an x-intercept of -2. Can you assist her?

Solution:

A line with a slope m has the general equation y = mx + c.

The x-intercept of the line is – 2.

Applying the formula of the x-intercept,

x = – $$\frac{c}{m}$$

-2 = – $$\frac{c}{6}$$       [Substitute the values of x and m]

c = 12           [Simplify]

If we combine the values of c and m, we get:

y = 6x +12

Hence, the equation of the line is y = 6x + 12.