Expressing a linear expression of a straight line in terms of slope of the line and intercept at horizontal axis is defined equation of a straight line in terms of slope and x-intercept.
A straight line often appears in geometry by passing through the horizontal axis of the Cartesian coordinate system at an -intercept. It makes the standard form of equation of the straight line to transform into some other form. In this case of straight line passing through the horizontal axis at an x-intercept, the equation of the straight line is usually expressed in terms of the slope of the straight line and x-intercept.
Assume, is a straight line which passes through the horizontal -axis at an -intercept by making some angle with the same horizontal axis.
Assume, the angle made by the straight line is theta . Also assume, the point of the straight line is intersected with the horizontal axis at a distance of units from the origin. Therefore, the coordinates of the point is . The point is one of the points of the straight line and also one of the points of the horizontal axis. Hence, the point is known -intercept. Assume, the coordinates of the point is .
Draw a perpendicular line from point and assume it intersects the horizontal axis at a point, which is assumed to call point . Thus, a right angled triangle, known is formed by the straight line geometrically.
According to the right angled triangle ,
The length of the opposite side is
The length of the adjacent side is
According to concept of the slope of the straight line, slope of a straight line is expressed in mathematical form as follows.
It can be written as follows.
It is an algebraic linear equation, which represents a straight line having some slope but it is passing through the horizontal axis at an -intercept.