## Intermediate Algebra for College Students (7th Edition)

Hence, the coefficient are $1,-2$.
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 $b$. $\frac{-a}{-2} = \frac{1}{2}$ $\frac{a}{2} = \frac{1}{2}$ $a=1$.