Given
The table,
To find the equation of the line.
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
[tex]y=mx+c[/tex]
It passes through (4,9).
That implies,
[tex]\begin{gathered} 9=m(4)+c \\ 4m+c=9\text{ \_\_\_\_\lparen1\rparen} \end{gathered}[/tex]
It passes through (16,6).
That implies,
[tex]\begin{gathered} 6=m(16)+c \\ 16m+c=6\text{ \_\_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]
Solving (1) and (2) implies,
[tex]\begin{gathered} (16m+c)-(4m+c)=6-9 \\ 16m-4m=-3 \\ 12m=-3 \\ m=-\frac{1}{4} \end{gathered}[/tex]
Substitute the value of m in (1).
That implies,
[tex]\begin{gathered} 4(-\frac{1}{4})+c=9 \\ -1+c=9 \\ c=9+1 \\ c=10 \end{gathered}[/tex]
Hence, the equation of the line is y= (-1/4)x+10.
