We know that there are infinite points in the coordinate plane. Consider an arbitrary point P(x,y)Â on the XYÂ plane and a line L. How will we confirm whether the point is lying on the line L? This is where the importance of equation of a straight line comes into the picture in two-dimensional geometry.
Equation of a straight line contains terms in x and y. If the point P(x,y) satisfies the equation of the line, then the point P lies on the line L.
Different forms of equations of a straight line
Equations of horizontal and vertical lines
Equation of the lines which are horizontal or parallel to the X-axis is y = a, where a is the y – coordinate of the points on the line.
Similarly, equation of a straight line which is vertical or parallel to Y-axis is x = a, where a is the x-coordinate of the points on the line.
For example, the equation of the line which is parallel to X-axis and contains the point (2,3) is y= 3.
Similarly, the equation of the line which is parallel to Y-axis and contains the point (3,4) is x = 3.
2. Point-slope form equation of line
Consider a non-vertical line LÂ whose slope is m, A(x,y)Â be an arbitrary point on the line and
-axis at a distance ‘a’ from the origin. Then the distance a is called the
\(\begin{array}{l}y\end{array} \)
– intercept of the line. The point at which the line cuts
\(\begin{array}{l}y\end{array} \)
-axis will be
\(\begin{array}{l}(0,a)\end{array} \)
.
Then, equation of the line will be
y-a = m(x-0)
y = mx+a
Similarly, a straight line having slope m cuts the X-axis at a distance b from the origin will be at the point (b,0). The distance b is called x- intercept of the line.
Equation of the line will be:
y = m(x-b)
5. Intercept form
Consider a line LÂ having x– intercept a and y– intercept b, then the line touches X– axis at (a,0)Â and Y– axis at (0,b).
You have learnt about the different forms of equation of a straight line. To know more about straight lines and its properties, log onto www.byjus.com.’
