$\text{Question: Find the equation of the line passing through the point } (-7,-4) \text{ and slope }m=4\text{. Then determine its }y\text{-intercept}$.$\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=-7\text{ and }y_0=-4\text{ and }m=4\text{.}$$\text{So the equation of the given line is }$$y-(-4) = 4(x-(-7))$$\text{or, }y+4=4(x+7)$$\text{or, }y+4=4x+28$$\text{or, }y=4x+28-4$$\text{or, }y=4x+24$$\text{The }y\text{-intercept of the line is }24$