# Reduce 4x-3y-12=0 to the "intercept form" and hence find its intercepts on the axis .

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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:

4x-3y-12=0

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.**

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