6.1 Straight line

  Basic Mathematics and Measurements

To draw a straight line we need minimum $2$ points.

The position of a point in a cartesian space is known as co-ordinate.

Similarly, $x-$ axis and $y-$ axis is known as co-ordinate axis.

The general equation of a straight line is,
$$y = mx + c$$
where,

$m = \tan \theta :$ Slope of the straight line
$c:$ Intercept made by the straight line on the $y-$ axis.

Slope: It is defined as the which the straight line makes with the positive $x-$ axis.

Slope of straight line joining two coordinates

The slope is given by,
$$\tan \theta = m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$$or$$\tan \theta = m = \frac{{{y_1} - {y_2}}}{{{x_1} - {x_2}}}$$

Equation of straight line joining two coordinates

The equation of a straight line can be written as,
$$\frac{{y - {y_1}}}{{x - {x_1}}} = m$$or$$\frac{{y - {y_2}}}{{x - {x_2}}} = m$$
where $m$ is a slope

Distance between any two coordinates

Distance between the two points is given by,
$$D = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} $$