X Intercept - Calculate, How To Find X Intercept On A Graph? - Cuemath

X Intercept

The x intercept for any curve is the value of the x coordinate of the point where the graph cuts the x-axis, or we can say that the x-intercept is the value of the x coordinate of a point where the value of y coordinate is equal to zero.

Let us learn more about the x-intercept along with its formula and examples.

1.	What is X Intercept?
2.	X Intercept Formula
3.	X Intercept on a Graph
4.	Find Equation of Line Using X Intercept
5.	FAQs on X Intercept

What is X Intercept?

In the linear equation, we read that the general form is represented as y = mx + b, where m and b are constants. The x-intercept is the point or the coordinate from where the line crosses and that lies at the x-axis of the plane. This means the y-coordinate value of the respective linear equation will always be equal to 0 when it crosses the x-axis. For x-intercept, the y-coordinate is zero and for the y-intercept, the x-coordinate is zero. the x-intercept is also known as horizontal intercept.

X Intercept Formula

There are various formulas and equations associated with intercepts. Below listed are a few general formulas mostly used. All these formulas are derived by substituting y = 0 in the equation and solving for x.

• The general form of a straight line is: ax+by+c=0, where a,b,c are constants. The x intercept of the line can be obtained by putting y = 0, x-intercept = −c/a
• The slope-intercept form of a straight line is: y = mx+c, where m is the slope of the line and c is the y-intercept. The x-intercept of the line can be obtained by putting y=0, x-intercept = −c/m
• The point-slope form of a straight line is y−b = m (x−a), where m is the slope of the line, (a,b) is a point on the line. The x-intercept of the line can be obtained by putting y = 0, x-intercept = (am−b)/m.
• The intercept form of a straight line is x/a + y/b = 1 where (a, 0) is its x-intercept and (0, b) is its y-intercept.

X Intercept on a Graph

To find the x-intercept of a line of the form y = mx+b, substitute y = 0.

Example: To calculate the x-intercept of any line for example the line y = 2x−4, put y = 0 in the equation of a line.

Solution:

0 = 2x−4 4 = 2x 2 = x

So, the x-intercept of the line y=2x−4 is 2

Similarly, by substituting x = 0, we can find the y-intercept y = 2(0)−4 y= -4

Find Equation of Line Using X Intercept

Let's consider an x-intercept example to understand the process behind how to find the x-intercept.

John wants to find the equation of a line with the slope equal to 2 and the x-intercept equal to -5. Can you help him?

The general equation of a line with slope m is y=mx+c. The x-intercept of the line is −5.

Using the formula of the x-intercept

x = - c/m -5 = -c/2 C = 10 on putting the value of c and m we have,

y = 2x +10 Equation of the line is y=2x+10

☛Related Articles:

Check out a few more articles closely connected to the x-intercept for a better understanding of the topic.

• x Intercept Calculator
• y Intercept Calculator