Question

A line passes through the points (-8, 1) and (-1, 6). A second line passes through the points (-3,0) and (-8,-5). What is the point of intersection of the two lines?

Answer 1

`\begin{gathered} y=mx+b \\ m=(6-1)/(-1+8)=(5)/(7) \\ 6=(5)/(7)(-1)+b \\ 6+(5)/(7)=b \\ b=(42+5)/(7)=(47)/(7) \\ y=(5)/(7)x+(47)/(7) \end{gathered}`

For the second line

`\begin{gathered} y=mx+b \\ m=(-5-0)/(-8+3)=(-5)/(-5)=1 \\ 0=1(-3)+b \\ b=3 \\ y=x+3 \end{gathered}`

The intersection will be

`\begin{gathered} y=(5)/(7)x+(47)/(7) \\ x+3=(5)/(7)x+(47)/(7) \\ x-(5)/(7)x=(47)/(7)-3 \\ (7x-5x)/(7)=(47-21)/(7) \\ (2x)/(7)=(26)/(7) \\ 14x=182 \\ x=(182)/(14) \\ x=13 \\ \\ y=13+3=16 \end{gathered}`

Therefore, the point of intersection is (13, 16)