$\text{Question: Find the equation of the line passing through the point } (-11,2) \text{ and slope }m=8\text{. Then determine its }y\text{-intercept}$.$\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=-11\text{ and }y_0=2\text{ and }m=8\text{.}$$\text{So the equation of the given line is }$$y-(2) = 8(x-(-11))$$\text{or, }y-2=8(x+11)$$\text{or, }y-2=8x+88$$\text{or, }y=8x+88+2$$\text{or, }y=8x+90$$\text{The }y\text{-intercept of the line is }90$