The x-intercept and y-intercept of the line equation can be derived by considering the point that gives the same slope as the given equation.
Recall that the general equation of a straight line may be given as y = mx + c
where m is the slope and c is the intercept
the slope is also the change in y divided by the change in x
From the equation 2x -3y - 6 = 0
2x - 6 = 3y
3y = 2x -6
y = 2x/3 - 2
comparing with the general equation, m = 2/3
Considering all the points, the slope of point
F = (-6 - 0)/0 - 3
= -6/-3 = 2
G = (-3 - 0)/(0 - 6)
= 1/2
H = (3-0)/(0 --2)
= 3/2
J = (-2 -0)/(0-3)
= 2/3
From above, point J has the same slope as equation hence the x intercept and y intercept of of the line equation are (3,0) and (0,-2)