Respuesta :
From the given table and options, we can note a linear behavior. Lets find the slope m and the y-intercept b for our table. As we know the line equation is
[tex]y=mx+b[/tex]where the slope m is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where the values on the right hand side come from 2 points of our table, for instance, we can choose points
[tex]\begin{gathered} (x_1,y_1)=(2,32) \\ (x_2,y_2)=(5,50) \end{gathered}[/tex]by substtuting these values into the slope formula, we get
[tex]m=\frac{50-32}{5-2}[/tex]which gives
[tex]\begin{gathered} m=\frac{18}{3} \\ m=6 \end{gathered}[/tex]then, our line equation has the form
[tex]y=6x+b[/tex]In order to find b, we must substitute one of the 2 choosen points, if we substitute point (2,32), we get
[tex]32=6(2)+b[/tex]then, we have
[tex]\begin{gathered} 32=12+b \\ 32-12=b \\ b=20 \end{gathered}[/tex]then, the searched line is
[tex]y=6x+20[/tex]which corresponds to the last option
