$\text{Question: Find the equation of the line passing through the point } (-6,6) \text{ and slope }m=2\text{. Then determine its }y\text{-intercept}$.$\text{Answer: }$$\text{The equation of the line passing through the point }(x_0,y_0) \text{ and slope }m \text{ is given by }y-y_0=m(x-x_0)\text{.}$$\text{In this problem }x_0=-6\text{ and }y_0=6\text{ and }m=2\text{.}$$\text{So the equation of the given line is }$$y-(6) = 2(x-(-6))$$\text{or, }y-6=2(x+6)$$\text{or, }y-6=2x+12$$\text{or, }y=2x+12+6$$\text{or, }y=2x+18$$\text{The }y\text{-intercept of the line is }18$