$\text{Question: Find the equation of the line passing through the point } (7,3) \text{ and slope }m=6\text{. Then determine its }y\text{-intercept}$.$\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=3\text{ and }m=6\text{.}$$\text{So the equation of the given line is }$$y-(3) = 6(x-(7))$$\text{or, }y-3=6(x-7)$$\text{or, }y-3=6x-42$$\text{or, }y=6x-42+3$$\text{or, }y=6x-39$$\text{The }y\text{-intercept of the line is }-39$