Question

Plot four lines to connect the points in adjacent quadrant

Answer 1

First, lets find the equation of the line that passes through the points (-4,3) and (-3,-5):

`\begin{gathered} slope\colon \\ m=\frac{-5-3}{-3-(-4)_{}}=(-8)/(1)=-8 \\ equation\colon \\ y-3=-8(x+4) \\ \Rightarrow y=-8(x+4)+3 \end{gathered}`

then, for the line that passes through (-3,-5) and (1,-4), we have:

`\begin{gathered} slope\colon \\ m=(-4-(-5))/(1-(-3))=(-4+5)/(1+3)=(1)/(4) \\ equation\colon \\ y+5=(1)/(4)(x+3) \\ \Rightarrow y=(1)/(4)(x+3)-5 \end{gathered}`

finally, for the line that passes through (1,-4) and (6,1), we get:

`\begin{gathered} slope\colon \\ m=(1-(-4))/(6-1)=(5)/(5)=1 \\ equation\colon \\ y+4=1\cdot(x-1) \\ \Rightarrow y=x-1-4=x-5 \\ y=x-5 \end{gathered}`

therefore, the equations are:

y = -8(x+4) +3

y = 1/4(x+3) -5

y = x-5