The standard equation of line graph is ax + by = c where a and b are the coefficient of x and y and c is the constant term. To draw a graph : It is drawn by converting the given linear equation in the form of y = mx + b where m is the slope and b is the y-intercept.
1) Slope = 0 then the line is horizontal line which is parallel to x –axis.
When the slope is zero then the equation of line will become y = b where b is any value. 2) Slope = infinitity or undefined then the line is vertical which is parallel to Y- axis.
When the slope is undefined then the equation of line is x = a where a is any value. 3) The equation of the line is in y= mx + b form.
For example x - 2y = -6
-2y = - x - 6 (add -x on both sides)
y = (-x - 6)/-2 ( divide both side by -2)
y = -x/-2 - 6/-2
y= ½ x +3
Here the slope m = 1/2 and
y intercept b= 3 , y -intercept means x coordinate is 0
Here first mark 3 on the y- axis as the slope is positive ½ so either go up 1 unit up and 2 units to right side from y –intercept or go down 1 unit and 2 units to left. In this way you will get 3 points (including y –intercept) .Join these points and you will get a required graph or a straight line- graph.
Note : If the slopes of two lines are same the lines are parallel to each other.
If the product of slopes is negative 1 (-1) then the lines are perpendicular to each other.