$\text{Question: Find the equation of the line passing through the point } (3,-5) \text{ and slope }m=-4\text{. Then determine its }y\text{-intercept}$.$\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=3\text{ and }y_0=-5\text{ and }m=-4\text{.}$$\text{So the equation of the given line is }$$y-(-5) = -4(x-(3))$$\text{or, }y+5=-4(x-3)$$\text{or, }y+5=-4x+12$$\text{or, }y=-4x+12-5$$\text{or, }y=-4x+7$$\text{The }y\text{-intercept of the line is }7$