Reduce 4x-3y-12=0 to the "intercept form" and hence find its intercepts on the axis .
4x - 3y - 12 = 0
The equation for the intercept form is:
y/a + x/b = 1
First let us move 12 to the right side:
==> 4x - 3y = 12
Now divide by 12:
==> x/3 - y/ 4 = 1
==x/3 + y/-4 = 1
Then x intercept a = 3
and y intercepy b = -4
4x-3y -12 = 0
To write the equation in intercept form we go as below:
0 = 4x-3y -12 . Add 3y to both sides
3y = 4x-12
y = (4/3)x -12/4 or y = (4/3)x-3 is the slope intercept form. 3/4 = slope and y = -3 is y intercept.
Double intercept form:
4x-3y -12 = 0
Add 12 to both sides.
4x-3y = 12. Divide by 12 both sises.
4x/12-3y/12 = 1. Rewrite as below:
x/(12/4) +y/(12/-3) = 1. Or
x/3 +y/(-3) = 1. This is the double intercept form of 4x-3y-12 = 0, where x= 3 and y = -3 are the intercept of the line on x and y axis respectively.
In otherwords, if ax+by+c = 0 is the equation of the line, then
ax+by = -c Or
ax/-c +by/-c = 1
x/(-a/c) +y/(-b/c) = 1. The intercept form of the equation.
Clearly If you put y = 0, x = -a/c and if ypou put x =0, then y = -b/c . So -a/c and -b/c are the intercepts of ax+by+c on x and y axis.
Any equation of the form x/k+y/l = 1 has the x intercept k and y inyercept l.
The general form of the equation of the line has to be reduced to the intercept form, that is:
x/a + y/b = 1
We'll write the given equation:
We'll add 12 both sides:
4x-3y = 12
We'll divide by 12 both sides, in order to obtain 1 to the right side:
4x/12 - 3y/12 = 12/12
x/3 - y/4 = 1
We'll re-write the equation:
x/3 + y/-4 = 1
So, the x intercept is 3 and the y intercept is -4.