$\text{Question: Find the equation of the line passing through the point } (-1,9) \text{ and slope }m=-8\text{. Then determine its }y\text{-intercept}$.$\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=-1\text{ and }y_0=9\text{ and }m=-8\text{.}$$\text{So the equation of the given line is }$$y-(9) = -8(x-(-1))$$\text{or, }y-9=-8(x+1)$$\text{or, }y-9=-8x-8$$\text{or, }y=-8x-8+9$$\text{or, }y=-8x+1$$\text{The }y\text{-intercept of the line is }1$