Intercept

The standard equation of a line in the cartesian coordinate system can be used to explain intercept meaning in mathematics. The point where the line intersects the coordinate axes is called an intercept. When a line crosses the X axis, the y coordinate of the crossing point is zero, and the intercept is known as the x intercept.

Similarly, the x coordinate of the point at where the line intersects the Y axis is zero, and the y coordinate of the point gives the line’s y intercept.

Intercept Form:

The x-intercept is the point on the x-axis where a line crosses it, and the y-intercept is the point on the y-axis where a line crosses it.

x/a + y/b = 1 is the intercept version of the equation of a line, where ‘a’ is the x-intercept and ‘b’ is the y-intercept. The x-intercept is the smallest distance between the origin and the point on the x-axis where the line crosses it, and the y-intercept is the shortest distance between the origin and the point on the y-axis where the line crosses it. Taking into account the points, the line cuts the x-axis at point(a, 0) and the y-axis at point (0, b).

The variables in the equation are x and y, and the x- and y-intercepts are a and b, respectively. The slope of this equation is -b/a.
Because this line intersects both coordinate axes, it forms a right triangle with them, and the area of a right angled triangle is equal to the product of half of its intercepts.  Furthermore, the intercept form of a line’s equation may be reduced and written as bx + ay = ab, which is the standard form of a line’s equation.

X-Intercept:

 The general version of the linear equation is written as y = mx + b, where m and b are constants. The x-intercept is the location or position on the x-axis of the plane where the line crosses. When the corresponding linear equation crosses the x-axis, the y-coordinate value will always be equal to 0. The y-coordinate for the x-intercept is zero, and the x-coordinate for the y-intercept is zero. The horizontal intercept is also known as the x-intercept.

Formula for X Intercept:

Intercepts are represented by a variety of formulae and equations. A few often used formulae are shown below. Substituting y = 0 in the equation and solving for x yields all of these formulae.
• A straight line has the general form ax+by+c=0, where a, b, c are constants.
Putting y = 0, x-intercept = -c/a will give you the line’s x intercept.
• A straight line’s slope-intercept form is y = mx+c, where m is the line’s slope and c is the y-intercept.
By placing y=0, x-intercept = c/m, the line’s x-intercept may be found.
• A straight line’s point-slope form is y-b = m (x-a), where m is the line’s slope and (a, b) is a point on the line.
By setting y = 0, x-intercept = (am-b)/m, the line’s x-intercept may be found.
• A straight line’s intercept form is x/a + y/b = 1, where (a, 0) is the x-intercept and (0, b) is the y-intercept.

Y-Intercept:

The y-intercept is the point where the graph crosses the y-axis. Finding the intercepts is crucial when graphing any function of the type y = f(x).

A function can have two different sorts of intercepts. These are x-intercept and y-intercept. These can be found by the intersecting points on the graph.

Steps to find y-intercept:

• We simply insert x = 0 in the equation to determine the y intercept of a function y = f(x).
• Find the value of y.
• Draw a point to represent the y-intercept (0, y).

Point slope form:
In point-slope form, the y-intercept
In point-slope form, the line’s equation is y-y1=m x-x1. We solve for y by substituting x=0 for the y-intercept.
y-y1 = m (0-x1)

 y-y1= – mx1

 y = y1 – mx1

The y-intercept of a line’s equation in point-slope form is thus: (0, y1 – mx1) or y1 – mx1.

Conclusion: 

The Intercept is a point  between the origin and the point where a coordinate axis crosses 

A graph’s intercepts are the locations where the graph crosses the axes. X-intercept is the point where the graph intersects the x-axis.

The y-coordinate is 0 at this position. 

 y-intercept is the point where the graph cuts the y-axis.