$\text{Question: Find the equation of the line passing through the point } (-9,1) \text{ and slope }m=2\text{. Then determine its }y\text{-intercept}$.$\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=-9\text{ and }y_0=1\text{ and }m=2\text{.}$$\text{So the equation of the given line is }$$y-(1) = 2(x-(-9))$$\text{or, }y-1=2(x+9)$$\text{or, }y-1=2x+18$$\text{or, }y=2x+18+1$$\text{or, }y=2x+19$$\text{The }y\text{-intercept of the line is }19$