Question

Which system of linear equations best represents the graph shown below? LIDS Է: IN 10 M 1.10 a »--x+ + 5 2 9 Ob y = 3x+ y = x+5 » 2 L = 3x+9 ос 2 - 3x+5 »--x+9 d 2+5 y-- - y---+ 9

Answer 1

Let:

`\begin{gathered} (x1,y1)=(0,5) \\ (x2,y2)=(3,7) \\ so\colon \\ m=(y2-y1)/(x2-x1)=(7-5)/(3-0)=(2)/(3) \end{gathered}`

Using the point-slope equation:

`\begin{gathered} y-y1=m(x-x1) \\ y-5=(2)/(3)(x-0) \\ y-5=(2)/(3)x \\ y=(2)/(3)x+5 \end{gathered}`

Let:

`\begin{gathered} (x1,y1)=(0,9) \\ (x2,y2)=(3,7) \\ m=(y2-y1)/(x2-x1)=(7-9)/(3-0)=-(2)/(3) \end{gathered}`

Using the point slope equation:

`\begin{gathered} y-y1=m(x-x1) \\ y-9=-(2)/(3)(x-0) \\ y-9=-(2)/(3)x \\ y=-(2)/(3)x+9 \end{gathered}`

Therefore, the system is:

`\begin{gathered} y=(2)/(3)x+5 \\ y=-(2)/(3)x+9 \end{gathered}`