Answer:
A = 8 and B = -2 and the equation is:
8x - 2y = -24
Explanation:
Line intercepts
Any non-horizontal and non-vertical line has two intercepts: The y-intercept is the point where the line crosses the y-axis, and the x-intercept is the point where the line crosses the x-axis, also called the zero or root.
We are given the equation:
Ax+By=-24
The x-intercept is (-3,0). Substituting the values of x and y:
A(-3)+B(0)=-24
Operating:
-3A = -24
Dividing by -3:
A = -24 / (-3) = 8
A = 8
The y-intercept is (0,12). Substituting and using the just-found value of A
8(0)+B(12)=-24
Operating:
12B = -24
Solving:
B = -2
Thus, A = 8 and B = -2 and the equation is:
8x - 2y = -24