Question

Which equation, written in the form of y = x + b, represents the table of values?

Answer 1

Let:

`\begin{gathered} (x1,y1)=(2,7) \\ (x2,y2)=(5,10) \end{gathered}`
`\begin{gathered} x=2,y=7 \\ 7=2m+b \\ ---------------- \\ x=5,y=10 \\ 10=5m+b \\ ---------- \\ Let\colon \\ 2m+b=7_{\text{ }}(1) \\ 5m+b=10_{\text{ }}(2) \\ (2)-(1) \\ 5m-2m+b-b=10-7 \\ 3m=3 \\ m=1 \end{gathered}`

Replace m into (1):

`\begin{gathered} 2(1)+b=7 \\ 2+b=7 \\ b=7-2 \\ b=5 \end{gathered}`

Answer:

`y=x+5`