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.
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
