Answer
Hence, the coefficients are $ -6,3 $.
Work Step by Step
Let the coefficients are $ a $ and $ b $.
Therefore, the equation will be.
$ ax+by=12 $ ... (1)
The standard $ y- $intercept form is
$ y=mx+c $
Isolate $ y $ in the equation (1).
$ y= \frac{-a}{b}x+\frac{12}{b} $
Where, $ y- $ intercept is $ \frac{12}{b} $.
In the question we have $ y- $ intercept $ 4 $ equate both.
$ 4 =\frac{12}{b} $
$ 4b=12 $
$ b=\frac{12}{4} $
$ b=3 $
Substitute the value of $ b $ into equation (1).
$ ax+3y=12 $
In the question we have $x- $ intercept $ -2$.
The point $ (-2,0) $ must satisfy the equation.
Plug the point into equation
$ a(-2)+3(0)=12 $
$ -2a+0=12 $
$ a = -6 $
