Question

It just the question number 32. Thank you please help

Answer 1

Given

The table,

To find the equation of the line.

Step-by-step explanation:

It is given that,

That implies,

The points representing the line is (4,9) and (16,6).

Therefore, the equation of the line is,pl

`y=mx+c`

It passes through (4,9).

That implies,

`\begin{gathered} 9=m(4)+c \\ 4m+c=9\text{ \_\_\_\_\lparen1\rparen} \end{gathered}`

It passes through (16,6).

That implies,

`\begin{gathered} 6=m(16)+c \\ 16m+c=6\text{ \_\_\_\_\_\_\_\lparen2\rparen} \end{gathered}`

Solving (1) and (2) implies,

`\begin{gathered} (16m+c)-(4m+c)=6-9 \\ 16m-4m=-3 \\ 12m=-3 \\ m=-(1)/(4) \end{gathered}`

Substitute the value of m in (1).

That implies,

`\begin{gathered} 4(-(1)/(4))+c=9 \\ -1+c=9 \\ c=9+1 \\ c=10 \end{gathered}`

Hence, the equation of the line is y= (-1/4)x+10.