Consider the standard form equation Ax+By=−24. If the x-intercept is (−3,0) and the y-intercept is (0,12), what are the values of A and B?

A = 8 and B = -2 and the equation is:

8x - 2y = -24

Step-by-step 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