Question

The ratio of the x and y intercepts made by the graph of the linear equation 2x + 3y = 9 on the x-axis and y-axis respectively is
(a) 2 : 3 (b) 1 : 3 (c) 3 : 2 (d) 3 : 1

Answer 1

Answer:

the correct answer is (c) 3 : 2

Step-by-step explanation:

2x + 3y = 9

2x/9 + 3y/9 = 1

x/4.5  y/3 = 1

Hence,

= 4.5 : 3

= 9 : 6

= 3 : 2

So the answer is (c) 3 : 2

Hope this helps u :))

Answer 2

Given:  

A straight line 2x + 3y = 9.

To Find:

The ratio of x-intercept and y-intercept on X and Y-axis respectively.

Solution:

The given problem can be solved by using the concepts of 2D coordinate geometry.

1. The given line 2x + 3y = 9, The ratio of x-intercept and the y-intercept is to be calculated.

2. Let a line ax + by + c = 0 be a straight line in a 2D coordinate system, the line intersects at the X-axis when the value of Y is 0 and it intersects The Y-axis when the value of X is 0.

Therefore, the value of x intercept = Value of x when the line touches the X-axis. (y = 0).

=> Value of x-intercept = ax + b (0) + c = 0,

=> Value of x-intercept = x = (-c/a).

   

        The value of y intercept = Value of y when the line touched the y-axis. ( x = 0 )

=> Value of y-intercept = a (0) + b(y) + c = 0,

=> Value of y-intercept = y = (-c/b).

3. Therefore, from the given line the x and y-intercepts can be calculated using the above formula.

=> x intercept = (9/2) = 4.5 units.

=> y intercept = (9/3) = 3 units.

4. The ratio of x intercept and y intercept is 4.5: 3,

=> 4.5: 3,

=> 1.5: 1,

=> 3: 2.

Therefore, the ratio of the x-intercept and the y-intercept is 3:2.