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# Intercept of a line

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 Sub Topics The intercept of a line is a Point in a graph which intersects either x axis or y axis. It can not cut both axes at a time. Now we will see how to find the line intercept with the help of formula: If we have a point on the line and the Slope of the line then the formula for finding the intercept of a line is: b = r – ms, where ‘m’ represents the Slope of the line. And ‘r’ and‘s’ are the coordinates of any point on the line. A number which measure the steepness of a line is known as Slope of a line. Generally slope of a line is denoted by m. It changes the value of y for small change in the ‘x’ along the line. Now we will see the formula for finding the slope of the line; Slope = m = Py - Qy , Px – Qx Where ‘x’ is the coordinate of point ‘P’ and ‘y’ is the coordinates of point ‘Q’. Now we will see how to find the intercept of a line. Suppose we have the value of ‘x’ and ‘y’ coordinates are 50 and 35 and slope of line is 2.5 then we can find the intercept of a line. We know that the formula for finding the intercept of a line: b = r – ms; Here the value of ‘r’ is 35 and the value of ‘s’ is 50; When we put the value of ‘r’ and ‘s’ in the given formula we get intercept of a line. b = r – ms; b = 35 – 2.5 * 50; b = 35 – 125; On further solving we get: b = -90; So the intercept of a line is -90.

## Define Intercept of a Line

The shortest distance measured between two points is known as straight line. If a line contains any curve then line is not straight. In mathematical Geometry a Straight Line is obtained by joining the two points.
Let’s see the equation of a straight line:
The equation of straight line is given by y = mx + c; where ‘m’ denotes the Slope of a line and y- intercept is given by ‘c’. The y - intercept is the Point on the y-axis where the given line crosses the y – axis, it means the point of Intersection of the line and y-axis. While determining the y-intercept there could be a possibility that the line lies on the origin or maybe not, but if it does then the y - intercept is already zero. If it doesn’t then we can calculate it by the equation of line. So in order to Define Intercept of a line we can use the equation of line which is shown below:
y = m(x) + c
e = [y - m(x)]
Where, (y) shows how far the line goes up,
(x) Denotes how far along and,
(m) Represents the Slope of line.
Let’s see some steps for calculating the y-intercept of line:
Step 1:- First put all the values which are required for the equation of line.
Step 2:- As we know that values are the coordinates of line and the Slope.
Step 3:- Then simplify if required for (c).
Let’s see how to find the y - intercept of a line, if the given values are y = -5, slope (m) of a line = 10 and x = 2?
As we know that the equation of line y = m(x) + c;
e = [y - m(x)]
e = [-5 - 10]
e = [-15]
So the intercept of a line is -15on given line.