Math Doubts

Equation of a straight line in terms of slope and X-intercept

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 x-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.

Geometrical Explanation

Assume, AB is a straight line which passes through the horizontal x-axis at an x-intercept by making some angle with the same horizontal axis.

Straight line passes through x-axis at an x-intercept

Assume, the angle made by the straight line is theta (θ). Also assume, the point A of the straight line is intersected with the horizontal axis at a distance of a units from the origin. Therefore, the coordinates of the point A is (a, 0). The point A is one of the points of the straight line and also one of the points of the horizontal axis. Hence, the point A(a, 0) is known X-intercept. Assume, the coordinates of the point B is (x, y).

Straight line passes through x-axis at an x-intercept forms a right angled triangle

Draw a perpendicular line from point B and assume it intersects the horizontal axis at a point, which is assumed to call point C. Thus, a right angled triangle, known ΔBAC is formed by the straight line AB geometrically.

  • The line segment AB becomes the hypotenuse of the right angled triangle ΔBAC.
  • The line segment AC becomes the adjacent side of the right angled triangle ΔBAC.
  • The line segment BC becomes the opposite side of the right angled triangle ΔBAC.

According to the right angled triangle ΔBAC,

tanθ = BCAC

The length of the opposite side is BC = y

The length of the adjacent side is AC = OC   –   OA = x  –  a

According to concept of the slope of the straight line, slope of a straight line is expressed in mathematical form as follows.

m = tanθ

m = BCAC

m = yx  –  a

It can be written as follows.

x  –  a = ym

x = ym  +  a

It is an algebraic linear equation, which represents a straight line having some slope but it is passing through the horizontal axis at an X-intercept.



Save (or) Share
Follow us
Email subscription
Math Doubts
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Mobile App for Android users Math Doubts Android App
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more