Find the ordered pairs for the x- and y-intercepts of the equation 2x − 6y = 24 and select the appropriate option below: a) the x-intercept is (2,0); the y-intercept is (0,-6). b) the x-intercept is (0,2); the y-intercept is (-6,0). c) the x-intercept is (12,0); the y-intercept is(0,-4). d) the x-intercept is (0,12); the y-intercept is (-4,0).

The x-intercept is found when y=0, and the y-intercept is found when x=0.  If y=0, then we have:

2x=24

x=12

Therefore, the x-intercept is 12, so the full coordinates are (12, 0).  Note that the only option with this x-intercept is C, so C is the correct answer.

You can find the y-intercept similarly.  If x is zero, then:

-6y=24

y=-4

Therefore, (0, -4) is the y-intercept.  This is also part of option C.