Mathematics
Grade-8
Easy

Question

The slope and y-intercept of the relation represented by the equation 12x – 9y + 2 = 0 are

  1. text  slope:  end text minus 4 over 3 comma y text -intercept:  end text minus 2 over 9
  2. text  slope:  end text minus 4 over 3 comma y text -intercept:  end text 2 over 9
  3. text  slope:  end text 4 over 3 comma y text -intercept:  end text minus 2 over 9
  4. text  slope:  end text 4 over 3 comma y text -intercept:  end text 2 over 9

Hint:

Linear equation in slope point form can be written as y = mx + c, where m = slope of the line and y-intercept = c.
We will simplify the given equation and compare the same with slope point form of an equation to find the value of its slope and y-intercept.

The correct answer is: text  slope:  end text 4 over 3 comma y text -intercept:  end text 2 over 9


    GIVEN EQUATION-
    12x - 9y + 2 = 0
    TO FIND-
    Slope and y-intercept.
    SOLUTION-
    We will simplify the given equation to bring it into the slope point form of an equation i.e. y = mx + c, where slope = m and y-intercept = c as follows-
    12x - 9y + 2 = 0
    ∴               -9y = -12x - 2 ................................ (Subtracting 12x and 2 from both sides)
    i.e.                y = -12/-9 x -2/-9 ....................... (Dividing both sides by -9)
    ∴                   y = 4/3 x + 2/9
    Comparing the above equation with y = mx + c, we get-
    Slope = m = 4/3 and y-intercept = c = 2/9.
    FINAL ANSWER-
    Option 'd' i.e. 'Slope: 4/3, y-intercept: 2/9' is the correct answer to the given question.

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