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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

x-intercept plotted on graph

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 Examples

Example 1: Shawn says that the line 2y=3x−6 has x-intercept equal to −3 and y-intercept equal to 2 while Judy says that the line has x-intercept equal to 2 and y-intercept equal to −3. Who is right?

Solution:

Given the line 2y=3x−6
x-intercept can be calculated by putting y = 0
2×0=3x−6
0=3x−6
6=3x
2=x

The x-intercept of the line is 2.

y-intercept can be calculated by putting x = 0
2y=3×0−6
2y=0−6
2y=−6
y=−3
The y-intercept of the line is -3.

Answer: ∴ Judy is right.
Example 2: A line with slope -2 passes through point P(a,1). If the sum of both the intercepts of the line is equal to 6, find the value of a.

Solution:

General equation for a line with a given slope and a point = y−b=m(x−a), where (a,b) is the point on the line.

y-1= -2(x-a)
x-intercept = 1/2 + a
y-intercept = 1 + 2a
Sum of intercepts = 1 + 2a + 1/2 + a
= 3a + 3/2
= 9/2 = 3a
= 3/2 = a

Answer: Value of a is 3/2
Example 3: Calculate the x-intercept of the parabola y=x²−3x+2.

Solution:

Put y=0 in the equation of a parabola. 0=x²−3x+2.
We can apply regular methods to solve a quadratic equation and calculate the value of x-intercepts.
x=2 and x=1 are the two roots of the equation.
It means that the graph is crossing the x-axis at two different points. So, x=2 and x=1 are the two x-intercepts of the parabola. Similarly, we can calculate the y-intercept by putting x = 0.

Answer: (2, 0) and (1, 0)

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Practice Questions on X Intercept

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FAQs on X Intercept

What do you Mean By x Intercept in Math?

The x-intercept means a coordinate plotted on the x-axis for any given curve. In other words, it 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.

How do you find the X Intercept in y = mx + b?

Here, y = mx + b is the slope-intercept form that can be used to identify the x and y-intercepts. The x-intercept is found by setting y = 0. On substituting the value of y =0, it gives the x-intercept value at which the line crosses the x-axis.

How do you Find x in an Equation?

If the given equation is of the form y = mx + b then we can easily find the value of x by putting the value of y=0 in any equation. The value of x so obtained is the x-intercept of the curve.

Can 0 be an x-Intercept?

Yes, 0 can be an x-intercept for the line y=mx, where m is the slope of the line and the value of x-intercept is equal to 0.

How to Find x-Intercept of a Parabola?

The x-intercept of any curve can be obtained using a similar technique. We just have to put the value of y as 0 in the equation of the curve. The general equation of a parabola is y=ax² +bx+c. We can calculate the x-intercept by putting y as 0.

How to Find the X-Intercept of any Line?

We know that equation of a line is of the form ax+by+c=0. To find the value of the x-intercept of the line we simply need to put the value of the y as 0.

What is the Value Angle Form Between Y and X Intercept of Line?

If the x-intercept and the y-intercept of a line are equal, then the line forms a 45 degrees angle with the x-axis.

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