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Find the x-intercept of the line 6x+2y=12

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2 Answers

(x,0) are coordinates of x-intercept.
(0,y) are coordinates of y-intercept
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1. 6x + 2 · 0 = 12 ---> 6x = 12 ---> x = 2
So, the x-intercept is (2 , 0)
6 · 0 + 2y = 12 ---> 2y = 12 ---> y = 6 .
     the y-intercept is (0 , 6)
2. 9x + 5 · 0 = 4 ---> 9x = 4 ---> x = 4/9 ; (4/9 , 0)
    9 · 0 + 5y = 4 ---> 5y = 4 ---> y = 4/5 ; (0 , 4/5)

Rearrange the equation of the line into slope-intercept form:     y = mx + b   ,

  where m is the slope of the line and b is the y-intercept (the y-intercept is the point where x= 0).

     6x + 2y = 12        subtract 6x from both sides of the equation 

     2y = -6x + 12       divide both sides of the equation by 2

     y = -3x + 6     ==>     y-intercept (b):   y = 6

Conversely, the x-intercept is the point where y = 0:

     y = -3x + 6

     0 = -3x + 6          add 3x to both sides of the equation

     3x = 6                 divide both sides of the equation by 3

     x = 2     ==>     x-intercept

The slope-intercept form of the line given by the equation 9x + 5y = 4 is as follows:

   5y = -9x + 4          after subtracting 9x from both sides of the equation, divide both sides by 5

   y = (-9/5)x + (4/5)

The y-intercept here is given by b; thus,   y = 4/5.

Solving for x when y = 0 yields the x-intercept:

     0 = (-9/5)x + (4/5)

     (9/5)x = (4/5)

     (5/9)(9/5)x = (4/5)(5/9)

     x = 4/9     ==>     x-intercept