$\text{Question: Find the equation of the line passing through the point } (-1,10) \text{ and slope }m=-6\text{. Then determine its }y\text{-intercept}$.$\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=-1\text{ and }y_0=10\text{ and }m=-6\text{.}$$\text{So the equation of the given line is }$$y-(10) = -6(x-(-1))$$\text{or, }y-10=-6(x+1)$$\text{or, }y-10=-6x-6$$\text{or, }y=-6x-6+10$$\text{or, }y=-6x+4$$\text{The }y\text{-intercept of the line is }4$