#### Answer

y=$\frac{-x}{2}$+5.5

#### Work Step by Step

For the purposes of this question, we will be using slope-intercept form, or as your teacher has most likely demonstrated, y=mx+b. In slope intercept form, the constant "m" represents the slope, and the constant "b" represents the y-intercept, or where the line crosses the y-axis.
Our first step will be to find "m" or the slope. We are given a line (x+2y=6), that is said to be parallel to the line we are looking for; this means the slopes are equal. If we use simple algebra to change the parallel line into slope-intercept form (subtract x and divide both sides by 2) we get y=$\frac{-x}{2}$+3. The slope of this equation is $\frac{-1}{2}$, so that will be the "m" of the equation we are trying to find.
Next, we will find "b" or the y-intercept. We were given that the point (1,-6) exists on our line. We can use the information we currently have to then find the y intercept. We will plug in 1 for x, -6 for y, and $\frac{-1}{2}$ for m. We end up with -6=( $\frac{-1}{2}$)(1)+b. If we solve this algebraically (by adding $\frac{1}{2}$) we get b=-5.5
Finally, we have to put all this together. We have found that m= $\frac{-1}{2}$, and b=-5.5. So our final answer is y=$\frac{-x}{2}$+5.5