Given:
Given a table.
Required:
To find the equation of the linear function.
Explanation:
From the table
[tex]\begin{gathered} (x1,y1)=(1,6) \\ (x2,y2)=(2,9) \end{gathered}[/tex]The general form of equation is
[tex]y=mx+b[/tex]Here the slope is
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x2} \\ \\ =\frac{9-6}{2-1} \\ \\ =\frac{3}{1} \\ \\ =3 \end{gathered}[/tex]So
[tex]y=3x+b[/tex]Now we have to find the value of b, by using the point (1,6)
[tex]\begin{gathered} 6=3(1)+b \\ \\ 6-3=b \\ \\ b=3 \end{gathered}[/tex]Now
[tex]y=3x+3[/tex]Final Answer:
The linear equation is
[tex]y=3x+3[/tex]