$\text{Question: Find the equation of the line passing through the point } (-8,-2) \text{ and slope }m=-1\text{. Then determine its }y\text{-intercept}$.$\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=-2\text{ and }m=-1\text{.}$$\text{So the equation of the given line is }$$y-(-2) = -1(x-(-8))$$\text{or, }y+2=-1(x+8)$$\text{or, }y+2=-1-x-8$$\text{or, }y=-1-x-8-2$$\text{or, }y=-1-x-10$$\text{The }y\text{-intercept of the line is }-10$