Mathematics
Grade-8
Easy

Question

For the line 4x – 3y – 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 any given line,
its x-intercept is a point where y-coordinate = 0 and
its y-intercept is a point where x-coordinate = 0

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


    GIVEN EQUATION-
    4x - 3y - 12 = 0
    TO FIND-
    Correct statement from the given options.
    SOLUTION-
    To find the x-intercept of the given line, we will substitute y = 0-
    4x - 3y - 12 = 0
    ∴ 4x - 3 (0) - 12 = 0
    ∴       4x - 0 -12 = 0
    ∴           4x - 12 = 0
    ∴                  4x = 12 ................................... (Adding 12 both the sides)
    ∴                    x = 12/4 ................................ (Dividing both sides by 4)
    ∴                    x = 3
    ∴     x-intercept = 3
    To find the y-intercept of the given line, we will substitute x = 0-
    4x - 3y - 12 = 0
    ∴ 4(0) - 3y - 12 = 0
    ∴      0 - 3y -12 = 0
    ∴         -3y - 12 = 0
    ∴                -3y = 12 ................................... (Adding 12 both the sides)
    ∴                    y = -12/3 ................................ (Dividing both sides by -3)
    ∴                    y = -4
    ∴     y-intercept = -4
    FINAL ANSWER-
    Option 'a' i.e. 'The x-intercept is 3, and the y-intercept is –4' is the correct answer to the given question.

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