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