The #x# intercept of a straight line refers to the (signed) distance from the origin of the point where the line intersects the #x# axis.

Now, all points on the given line must satisfy the equation

#3y=2x+24#

On the other hand, any point on the #x# axis must satisfy #y=0#. Thus, to obtain the #x# intercept of a straight line we must substitute #y=0# in its equation.

This gives

#2x+24=0#

and thus #x=-12#.

Similarly, substituting #x=0# gives the #y# intercept as +8.

Alternatively, we could have expressed the equation of the straight line in the form #x/a+y/b=1# and directly read off the values of #a# and #b# as the #x# and #y# intercepts, respectively.

In this case, rearranging and dividing both sides by 24 gives

#3y-2x =24 implies {3y-2x}/24=1 implies y/8 - x/12=1#

or

#x/{-12} +y/8=1#