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

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fakeyelid | Student, Grade 10 | eNoter

Posted August 14, 2010 at 4:30 PM via web

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

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giorgiana1976 | College Teacher | Valedictorian

Posted August 14, 2010 at 4:35 PM (Answer #1)

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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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neela | High School Teacher | Valedictorian

Posted August 14, 2010 at 4:57 PM (Answer #2)

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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.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted August 14, 2010 at 7:24 PM (Answer #3)

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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

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