$\text{Question: Find the equation of the line passing through the point } (-10,2) \text{ and slope }m=6\text{. Then determine its }y\text{-intercept}$.$\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=-10\text{ and }y_0=2\text{ and }m=6\text{.}$$\text{So the equation of the given line is }$$y-(2) = 6(x-(-10))$$\text{or, }y-2=6(x+10)$$\text{or, }y-2=6x+60$$\text{or, }y=6x+60+2$$\text{or, }y=6x+62$$\text{The }y\text{-intercept of the line is }62$