$\text{Question: Find the equation of the line passing through the point } (-4,1) \text{ and slope }m=7\text{. Then determine its }y\text{-intercept}$.$\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=-4\text{ and }y_0=1\text{ and }m=7\text{.}$$\text{So the equation of the given line is }$$y-(1) = 7(x-(-4))$$\text{or, }y-1=7(x+4)$$\text{or, }y-1=7x+28$$\text{or, }y=7x+28+1$$\text{or, }y=7x+29$$\text{The }y\text{-intercept of the line is }29$