$\text{Question: Find the equation of the line passing through the point } (6,10) \text{ and slope }m=-9\text{. Then determine its }y\text{-intercept}$.$\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=6\text{ and }y_0=10\text{ and }m=-9\text{.}$$\text{So the equation of the given line is }$$y-(10) = -9(x-(6))$$\text{or, }y-10=-9(x-6)$$\text{or, }y-10=-9x+54$$\text{or, }y=-9x+54+10$$\text{or, }y=-9x+64$$\text{The }y\text{-intercept of the line is }64$