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 mand bare 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 formof 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
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 yas 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.
