# 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,

$\stackrel{↔}{AB}$

is a straight line which passes through the horizontal

$x$

-axis at an

$x$

-intercept by making some angle with the same horizontal axis.

Assume, the angle made by the straight line is theta

$\left(\theta \right)$

. 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

$\left(a,0\right)$

. 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

$A\left(a,0\right)$

is known

$X$

-intercept. Assume, the coordinates of the point

$B$

is

$\left(x,y\right)$

.

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

$\Delta BAC$

is formed by the straight line

$\stackrel{↔}{AB}$

geometrically.

• The line segment
$\stackrel{‾}{AB}$

becomes the hypotenuse of the right angled triangle

$\Delta BAC$

.

• The line segment
$\stackrel{‾}{AC}$

becomes the adjacent side of the right angled triangle

$\Delta BAC$

.

• The line segment
$\stackrel{‾}{BC}$

becomes the opposite side of the right angled triangle

$\Delta BAC$

.

According to the right angled triangle

$\Delta BAC$

,

$tan\theta =\frac{BC}{AC}$

The length of the opposite side is

$BC=y$

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.

$m=tan\theta$

$⇒m=\frac{BC}{AC}$

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

$X$

-intercept.