$\text{Question: Find the equation of the line passing through the point } (-5,5) \text{ and slope }m=-8\text{. Then determine its }y\text{-intercept}$.$\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=-5\text{ and }y_0=5\text{ and }m=-8\text{.}$$\text{So the equation of the given line is }$$y-(5) = -8(x-(-5))$$\text{or, }y-5=-8(x+5)$$\text{or, }y-5=-8x-40$$\text{or, }y=-8x-40+5$$\text{or, }y=-8x-35$$\text{The }y\text{-intercept of the line is }-35$