Mathematics
Grade-8
Easy

Question

For the line 3x – 4y – 12 = 0, which statement is true?

  1. The x-intercept is 3, and the y-intercept is 4
  2. The x-intercept is 3, and the y-intercept is –4
  3. The x-intercept is 4, and the y-intercept is 3
  4. The x-intercept is 4, and the y-intercept is –3

Hint:

For a given line-
1. x-intercept is the value of x-coordinate for which y = 0 and
2. y-intercept is the value of y-coordinate for which x = 0.

The correct answer is: The x-intercept is 4, and the y-intercept is –3


    GIVEN-
    Given line - 3x – 4y – 12 = 0
    TO FIND-
    True statement from the given options.
    SOLUTION-
    We substitute x = 0 and y = 0 in the given equation to find the value of x-intercept and y-intercept, respectively.
    For y-intercept-
    3x – 4y – 12 = 0 ............... (given)
    ∴ 3 (0) - 4y - 12 = 0
    ∴           -4y - 12 = 0
    ∴                  -4y = 0 + 12 .......... (Adding 12 both the sides)
    ∴                  -4y = 12
    ∴                    y = -12/4 ............. (Dividing both sides by -4)
    ∴                    y = -3

    For x-intercept-
    3x – 4y – 12 = 0 ............... (given)
    ∴ 3x - 4 (0) - 12 = 0
    ∴       3x - 0 - 12 = 0
    ∴                   3x = 0 + 12 .......... (Adding 12 both the sides)
    ∴                   3x = 12
    ∴                     y = 12/3 ............. (Dividing both sides by 3)
    ∴                     y = 4
    FINAL ANSWER-
    Option 'd' i.e. 'The x-intercept is 4, and the y-intercept is –3' is the correct answer to the given question.

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