# Equations of Straight Lines

## Equations of Straight Lines

## Fundamentals of Straight Line Equations

- The
**equation of a straight line**in the Cartesian coordinate system traditionally takes the form y=mx+c. Here, ‘**m**’ stands for the slope, or gradient of the line, while ‘**c**’ is the y-intercept - the point where the line crosses the y-axis. - The
**slope**of a line can be determined using two points on the line, (x1,y1) and (x2,y2), employing the formula: m = (y2 - y1) / (x2 - x1). - A line’s
**y-intercept**is found by setting x to 0 in the line’s equation and solving for y.

## Intercepts and Intersection Points

- An
**x-intercept**is the point where the line crosses the x-axis, it is found by setting y to 0 in the equation of the line and solving for x. - When the equation for two lines are set equal to each other and solved, this yields the coordinates of the
**intersection point**of these two lines.

## Characteristics of Parallel and Perpendicular Lines

- If two lines are
**parallel**, then their slopes, or gradients, are equal. - If two lines are
**perpendicular**, the product of their gradients is -1. Hence, the gradient of a perpendicular line is the negative reciprocal of the original line’s gradient.

## Special Forms of the Equation of a Straight Line

- The
**point-slope form**of the equation of a straight line allows you to create the equation from a known slope and a single known point on the line - y-y1 = m(x-x1). - The
**two-point form**is equally useful. When two points on the line are known, this form can be used - (y - y1) = ((y2 - y1) / (x2 - x1)) * (x - x1). - You can use the
**intercept form**to create the equation of a straight line from its x and y intercepts - x/a + y/b = 1.

## Real-world Application of Straight Line Equations

- The principles of
**coordinate geometry**and the equation of straight lines are not exclusive to mathematical problems. They have myriad applications in real life - from calculating the shortest distance between places, to devising optimal travel routes, managing logistics and even in computer graphics and physics. - The knowledge of the
**intersection point of two lines**plays a key role in many physics concepts and are heavily used in graphic designing and animation, where the intersection points determine the way images and vectors interact.