$\text{Question: Find the equation of the line passing through the point } (7,7) \text{ and slope }m=5\text{. Then determine its }y\text{-intercept}$.$\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=7\text{ and }y_0=7\text{ and }m=5\text{.}$$\text{So the equation of the given line is }$$y-(7) = 5(x-(7))$$\text{or, }y-7=5(x-7)$$\text{or, }y-7=5x-35$$\text{or, }y=5x-35+7$$\text{or, }y=5x-28$$\text{The }y\text{-intercept of the line is }-28$