Answer
Hence, the coefficient are $ 1,-2 $.
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 $ -6 $ equate both.
$ -6 =\frac{12}{b} $
$ -6b=12 $
$ b=\frac{12}{-6} $
$ b=-2 $
And the slope is $\frac{-a}{b}$.
In the question we have $ \frac{1}{2} $ equate both.
$ \frac{-a}{b} = \frac{1}{2} $
Substitute the value of $ b $.
$ \frac{-a}{-2} = \frac{1}{2} $
$ \frac{a}{2} = \frac{1}{2} $
$ a=1 $.
