What is the equation of the line with x and y intercepts 4 and 7 respectively.  

Expert Answers
justaguide eNotes educator| Certified Educator

The x and y intercepts of the line are 4 and 7. Therefore the line passes through the points (4, 0) and (0, 7)

The equation of the line between the points (4, 0) and (0, 7) is given as (y – 0) = [(7- 0)/ (0 – 4)] (x – 4)

=> y = (7/-4) (x- 7)

=> y = (-7/ 4) (x – 7)

=> 4y = -7x + 28

=> 7x + 4y – 28 = 0

The required line with x and y intercepts 4 and 7 is 7x + 4y – 28 = 0.

neela | Student

The equation of the line with x and y in the standard double intercept form is x/a+y/b = a. Where  intercept is a, and y intercept is b.

Therefore the equation of the line  with x intercept 4 and y interceppt 7 is x/4 +y/7 = 1.

We check whether this is true:

x intercept is got by putting y= 0 in x/4+y/7 = 1:

 So x/4 + 0/7 = 1,, So x/4 = 1, or x= 4.

We check whether y intercept is 7: We get y intercept by putting x = 0 in x/4+y/7 = 1. So,  0/4+y/7 = 1, or y/7 = 1. So y = 7.

Therefore x/4+y/7 = 1 is the required equation. We write the equation  in  ax+by+c = 0 form by mutiplying  x/4+y/7 = 1 by 4*7 = 28 :

28(x/4+y/7) = 1*28. This gives us the equation,7x +4y = 28. Or 7x+4y-28 = 0.