Question

If the graph of the linear equation 24x + 7y = 168
cuts the x-axis and y-axis at A and B respectively,
then length of AB is equal to
(1) 25 units
(2) 7 units
(3) 24 units
(4) 31 units​

Answer 1

Note:

x, y-intercept form of the line :

The equation of a line in x, y-intercept form is given as ; x/a + y/b = 1

where, a is the x-intercept and b is the y-intercept.

Here,

The given linear equation is ;

=> 24x + 7y = 168.

=> 24x/168 + 7y/168 = 168

=> x/7 + y/24 = 1

Hence,

The x, y-intercept of the given linear equation is x/7 + y/24 = 1.

Here,

7 is the x-intercept and

24 is the y-intercept.

Here ,

It is said that the graph of the given linear equation cuts the x-axis at point A and y-axis at point B.

Thus,

Point of interception on x-axis will be;

A(7,0).

Point of interception on y-axis will be;

B(24,0).

Hence,

The length of the segment AB will be;

=> AB = √(7^2 + 24^2)

=> AB = √(49 + 576)

=> AB = √625

=> AB = 25 units.

Hence,

The required answer is : option (1)