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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

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

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 = \(\frac{-C}{m}\)

**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.

Frequently Asked Questions

When an equation is given in the form, y = mx + b, we can quickly determine the value of x by setting the value of y to 0. The obtained value of x is the x-intercept of the equation.

The x-intercept is the value of the x coordinate of a point on a plane where the value of the y coordinate is zero. It is the value of the x coordinate of the point where the graph intersects the x-axis.

Yes, 0 can be the x-intercept for the line y = mx, where ‘m’ denotes the slope of the line and x-intercept equals 0.