$\text{Question: Find the equation of the line passing through the point } (8,-9) \text{ and slope }m=2\text{. Then determine its }y\text{-intercept}$.$\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=8\text{ and }y_0=-9\text{ and }m=2\text{.}$$\text{So the equation of the given line is }$$y-(-9) = 2(x-(8))$$\text{or, }y+9=2(x-8)$$\text{or, }y+9=2x-16$$\text{or, }y=2x-16-9$$\text{or, }y=2x-25$$\text{The }y\text{-intercept of the line is }-25$