Intercept in Circle

An intercept in mathematics is a location on the y-axis through which the line’s slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written asy = mx+c, where m denotes slope and c denotes the y-intercept.

Exploring Intercept In Circle

The term “intercept” refers to the location where a line or curve crosses a graph’s axis. x intercept is the point at which the x-axis is crossed. The y-intercept is the point at which they axisis crossed.

The x or y axis intersection point is what is meant when a line has an intercept. The   y-axis is often taken into account if the axis is not stated. The letter “b” is typically used to represent it.

Because the line is precisely vertical, regardless matter how far off the top or bottom of the chart it is, it will always intersect the y-axis someplace.

Intercept Method

Y = mx + c is the equation for the line that crosses the y-axis at a certain position.

We may swap out c for b when writing the intercept form of the line. As a result, the equation is:

y = mx + b

Therefore, b = y – mx is the formula for a line y-intercept.

Where y and x are the points ony-axis and x-axis, respectively, and b is the intercept, m is the line’s slope.

Taking into account that a line intersects the x- and y-axes at points a andb, respectively, there is another method to write the equation of the line.

x/a + y/b = 1

Here x-axis and y-axis are intersected by the line at points a andb, respectively. The positions of the locations where the line crosses both axes with relation to the origin are explained by the values of a andb, which might be positive, negative, or zero.

Intercept Form for Slope

The line with a slope of m and an intercept of c on y-axis has the equation:

y = mx + c

Because the intercept is depicted on the positive or negative sides of the y-axis, respectively, the value of c might be either positive or negative.

Graph intercepted

The points on a graph where the graph crosses the two axes are known as the intercepts(x-axis and y-axis). The x-coordinate is the point where the graph crosses the x-axis, and the y-coordinate is the point where the graph crosses the y-axis.

The line that has intercepts a and b on the  x- and y-axes, respectively, has the equation:

x/a + y/b = 1

Example 

Letx-axis and y-axis be intersected by two interceptsP(2,0) and Q(0,3), respectively. Find the line’s equation.

Given, the x-axis and y-axis are intersected by two interceptsP(2,0) and Q(0,3).

Using the line’s known equation,

x/a + y/b = 1 ……….. (1).

Here, a = 2 and b = 3.

As a result, when we enter the intercept values a and b into equation1, we obtain:

=>x/2 + y/3 = 1.

=> 3x + 2y = 6.

=> 3x + 2y – 6 = 0,.

Consequently, the line’s equation is 3x + 2y – 6 = 0.

Intercept in circle

Lety=0, then use the x-intercept formula to get it. Let x=0 and then work out y to find ay-intercept. Find the circle’s intercepts using the above equation as an example.

Intercept of line on circle

Where the graph contacts or crosses thex-axis is known as the x-intercept. Where the graph contacts or crosses the y-axis is known as the y-intercept. Let y=0, then use the x-intercept formula to get it.

y-intercept of circle formula

Where the graph contacts or crosses the y-axis is known as the y-intercept. Let y=0, then use the x-intercept formula to get it. Let x=0 and then work out y to find a y-intercept.

Conclusion

The y-intercept is the point at which  y-axis is crossed. The x-coordinate is the point where the graph crosses thex-axis, and the y-coordinate is the point where the graph crosses the   y-axis. The positions of the locations where the line crosses both axes with relation to the origin are explained by the values of a andb, which might be positive, negative, or zero.