$\text{Question: Find the equation of the line passing through the point } (10,-6) \text{ and slope }m=10\text{. Then determine its }y\text{-intercept}$.$\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=10\text{ and }y_0=-6\text{ and }m=10\text{.}$$\text{So the equation of the given line is }$$y-(-6) = 10(x-(10))$$\text{or, }y+6=10(x-10)$$\text{or, }y+6=10x-100$$\text{or, }y=10x-100-6$$\text{or, }y=10x-106$$\text{The }y\text{-intercept of the line is }-106$